What we seek is information confirming that a given town did keep blacks out [if it did!], either through the use of restrictive covenants throughout the town, violence or threats of same, bad behavior by white individuals, an ordinance, realtor steering, bank redlining, or other formal or informal policies.
While we are only interested in exclusion, such exclusion need not be total. The book, Sundown Towns, has a chapter telling how a town may have driven out its blacks, even posted the traditional sundown town sign, yet allowed one family to remain. Larger cities have even allowed more than one, in a way. Cicero, IL, for example, when burning out a would-be black apartment renter, had some 40 blacks in town -- probably as servants in white households, in such institutions as jails, hospitals, colleges, etc., or as renters in large apartment houses not really located in residential neighborhoods and hence below the radar of whites. Since Cicero defined itself as all-white and took steps to keep out the next black would-be household, it certainly qualifies. Therefore, while doing census research, take care to notice non-household blacks. Their existence does not take a town off the roll of suspected sundown communities.
Also, although in the past many sundown towns kept out other groups, such as Mexicans, Asian Americans, Jews, etc., today most sundown towns have accepted all but blacks. However, we are still interested in them because they kept out (and may still keep out) blacks. Finally, some towns have given up being sundown, usually between 1970 and today, yet we are still interested in them owing to their past.
A first step, then, is to look up the census information on racial composition in various years. Data at census.gov provide the racial proportions of every town in the country with more than a few hundred inhabitants for 1990 and 2000. Included is information as to age and sex in the black population and number of households with black adult householders. This information is particularly useful because it allows us to avoid misattributing residential status to African Americans living in institutions such as colleges or prisons or within white households as servants. For 1860-1980, the racial composition of your town will be in the printed census in the bound volumes of the census, probably at your local library and certainly at your nearest university library. Get the actual census figures, decade after decade. They are also online at http://www.census.gov/prod/www/decennial.html. However, in some years breakdowns by race are provided only for towns larger than 2,500 and in one decade only for towns larger than 4,000. For smaller towns, you can count the number of blacks listed in the "manuscript census," described in the next paragraph, for 1930 and prior decades.
For small towns, the census in many years, especially before 1940, does not list population by race, but you can amass it yourself from the "manuscript census" for any decade between 1860 and 1930 inclusive (except 1890, most of which was destroyed by fire). This is the raw data of the census; much of it is on the web at various sites, usually by state. Large libraries and genealogical collections also have it on microfilm. You may find sharp drops in black population, which are of course suspicious. If you only find low numbers of blacks, decade after decade, that too is suspicious, especially if blacks are hardly absent from nearby towns and counties or if the town's total population is increasing.
A free website, Social Explorer, https://www.socialexplorer.com/explore-maps, provides a lot of census information in readable format.
Local histories, newspapers
Then go to the local libraries (in person) and read (skim) any local history books, such as centennial histories and county histories. Usually the local library has a local history room (or local history shelf, in small libraries). Probably you will find NOTHING about blacks, but sometimes there are surprises. If there are notes on file from the WPA Federal Writers Project (c.1935-40), skim those. Also, see if there are vertical files (newspaper clippings) on "blacks," "Negroes," "segregation," "Ku Klux Klan," or other related topics.
Then you can scan local newspapers for the decade between two adjacent censuses that show a sharp decline in black population, to see if it describes any actions whites took to cause the decline. Sometimes the nearest newspaper outside the town in question will be more forthcoming.
Then ask the librarian in charge of the local history collection if s/he knows anything about the absence of blacks. Has s/he ever heard it might have been on purpose? Does s/he know of any stories (oral history) about anything bad that happened to a black family that tried to move into the town in the 1920s, 1970s, or any other decade?
Follow up by asking the librarian, "Who knows the most about the history of the town?" Every town has an expert. Then interview (in person) that person or persons. Ask, "who else should I talk with?" Is there a genealogical society? If so, attend its next meeting, after talking with its leader. Begin softly, maybe by asking what the town's major employers used to be. Eventually ask, "Have you ever heard that [name of town] used to keep out blacks?" Maybe mention that some nearby towns (by name) used to keep out blacks, and follow by asking if this community had the same policy. If folks say yes, then ask how they heard it, from whom, about when (year), etc.
Oral history is fine, so long as it is solid. Thus, if a person says "Blacks were not allowed..." then s/he should be asked, "How do you know that?" Also, seek details: "Did you ever hear of any family that moved in, then left?" etc. Do also seek written sources, such as some ordinance about keeping out blacks (or another group). The "ordinance," however, may be nothing more than a motion voted on in a city council meeting on a Tuesday evening in 1911, perhaps not even noted in the minutes of that meeting, and certainly almost impossible to find now.
Repeat this process with the City Clerk and the head of the local historical society. Bear in mind, however, particularly with a local history society, that this usually does not work UNLESS you are there in person. Usually these folks just don't want to say anything bad about their town if they can help it. In person, however, they don't want to lie. And of course, you flatter them by telling them (correctly) that they are the expert on the town's history. Another good idea: go to the local nursing home, or to places where seniors live or hang out (community center, SRO hotel). Interview elderly people. Take good notes, including "quote notes" (with "") when you actually capture the phrase verbatim. Old folks love to hold forth on the long-ago past. Also talk with long-time realtors, minority group members in nearby towns, and other likely sources. In general, email folks does not work, not on a ticklish subject. It only sets off respondents' alarms and they reply carefully if at all. Leaving phone messages is only slightly better. You need to talk with people, face to face if possible, on the phone if face-to-face is not possible.
Always we must recall that a community's overwhelming whiteness might be an accident, that perhaps no African Americans ever happened to go there. We cannot classify an "all-white town" as a "sundown town" unless we have evidence about its racial policies. Moreover, one must use common sense and historical and sociological knowledge in this work. Lemhi County, in northern Idaho, all-white in 1930, appears less suspicious than Garrett County, in western Maryland, which had 24 African Americans in that year, because 13 other Idaho counties also had no African Americans, while other Maryland counties all had more than 1,000. But then, a historian whose parents were born and raised in Lemhi County wrote that according to her relatives, "Black people were 'run off' in some distant past." Meanwhile, several sources, including Henry Louis Gates Jr., confirmed that Garrett was a sundown county. So, suspicion is appropriate in both cases, and additional sources have solidly confirmed Garrett.
Happy hunting; we await your results!