I'm working with some data at the 2010 Voting Tabulation District level (like the 2010 Census, Vote, and Enrollment data on this page). I'd like to merge in some information about US House districts, and I'm looking for an easy way of seeing which Congressional district each VTD belongs in. I could grab the district shapefiles and do this with GIS, but worry about it being messy and imperfect. Is there a relationship file somewhere that maps 2010 New York State VTD's into 2010 NYS Congressional districts? I'm thinking of something like the Census' Congressional District Relationship Files, but for VTD's.
You can get block assignment files for a given state from this Census Bureau page
In those files, there are block assignments for all of the geographies which need to be assigned. You should be able to "join" the VTD and CD tables on common block IDs to get what you need.