Why would a correspondence chess player be accused of using a computer? I play a good deal of online correspondence chess. On the website I use I sometimes see users being accused of using computers in correspondence chess, but without any evidence being presented.

What is the basis for such accusations? How can one find out whether a correspondence chess player uses a computer?
The basis for such accusations is usually hurt pride.

That being said, if a player consistently plays moves proposed by a particular engine, you can be pretty sure that the engine is the source of these moves. But for such an assessment one game usually isn't enough and it is definitely possible to use an engine without leaving these tell-tale signs.