Eugene Volokh writes, regarding the prosecution of two Unitarian minister in New Paltz, NY for marrying same-sex couples:

Some readers suggest that the clergy may be being prosecuted for signing their names to some government document attesting to the marriage. This might indeed be more punishable as an offense, partly because it’s more likely to be seen as a false statement of fact—a clerk might indeed not realize on a quick glance that this is a same-sex marriage, and be confused into thinking that the marriage was valid. But that’s not what I understood “solemnizing” to mean under New York law; as I understand it, solemnizing means performing the marriage, not signing a document.

This prompted me to dig up my New York marriage certificate from August, 1995. There’s a signature on it by the town clerk who issued it, but no place on the certificate for the signature of the person who performed the ceremony. (The town clerk happened to be the person who performed the ceremony, but if someone else had, there’s no place on the certificate for that person to sign.) For that matter, there’s no place on the certificate for the couple to sign, and I seem to recall signing something at some point. The wording on the certificate alludes to a “duly registered license … on file in this office.” Perhaps the person who performs the ceremony has to sign the duly registered license.