Can crows see in ultraviolet? If so, does their plumage look different in UV?
Corvids (and raptors) are reported to not see UV Håstad et. al. 2005.

However, American crows are reported to recognize sex-specific differences in plumage that are invisible to humans Eaton 2006.

Unfortunately, I don't have access the latter paper so I don't know what the basis for that discrimination is or how to reconcile that result with those of Håstad et. al.

You might also find this well referenced blog post that summarizes these results to be of interest.