Democrat going all the way back to 1932, at least (though the off chance of voting Republican in 56 considering African-Americans can't vote). Before that, I'm guessing Democratic still, kind of a Southern thing with backlash against the Republicans. I'm guessing it would vote similarly to Maryland.
I wouldn't be so quick to assume that blacks couldn't vote in DC 1956. Before the Voting Rights Act, there were black voters (they were key to Truman's 1948 victory). It was only in certain locations, many in the Deep South, where blacks were stopped by local authorities. By the 1950s, even many anti-Civil Rights officials, such as Louisiana Governor Earl Long, advocating giving blacks the vote (presuming that this would mean more votes for them). Anybody know the racial makeup of DC back then?