Today we received background checks from NY State. The background check itself was still blank. But it was accompanied by a letter than was signed and notarized that said that the background check would be blank. Odd. They can notarize a letter but can't notarize the background check. So I stapled them together and sent them off for apostille by the NY Secretary of State.
Unfortunately, even though I asked for the background check to be listed in my wife's married name and maiden name, they only came in her married name. Since she never used that name while living in NY, that could be a problem for the consulate or for Rome. So I sent a letter thanking them for sending the notarized background check but asking for another one in her maiden name.