In my election, we had to pick a bunch of judges. There were 8 positions up for election in one court. There were 8 democrats listed and 1 republican. That one republican was ALSO listed as a democrat - he registered under both parties. So it didn't matter who you voted for.
In some small elections such as those for town offices, often it's just a matter of not enough people interested. Many offices are not really contested at all, but have to go though an election legally anyway. In some cases if the candidate is liked by the oppostion, they'll endorse him and he'll run on both tickets, but otherwise the opposition will just be blank. It seems to depend partly on how the parties relate. I don't remember when I last saw a two party endorsement here, but when I lived in a small town in Connecticut, and held several town positions, it was done with some regularity. It's often the case for Town Clerks. If you get a good one, party is irrelevant.
Connecticut has a minority representation rule, such that if a board has, say, three members, at least one must be of a different party than the majority. Two for a board of five, and so forth. The result is that in some towns either a full slate is not run on one party, or a double party endorsement is made, or, if they can't come to an agreement or don't know ahead of time who will get the most votes, a losing minority candidate can win the position over the lowest-scoring majority candidate. In my career in Connecticut, I had all three instances. I won an office or two despite being in the minority party by a margin of one to two and coming in last, I won an office or two by being the third of three total candidates, and (proud to say) I got a couple of two party endorsements also.
In many small towns, owing to the low interest and the minority representation rule, the election is often really in the party caucus.
