This is all I can find about bows (I only looked out of idle curiosity, nothing to do with your family friend). There doesn't appear to be a NYC regulation, but the state says (save the last about the crossbow, these are about hunting with them here, not owning.) -
A hunter education course is required for persons who cannot show proof that they have ever possessed a hunting license. The general course is a minimum 10 hours in length....
Hunters wishing to bowhunt for deer and bear must take an additional 8 hour minimum bowhunter education course...
Crossbows are illegal. Except for Modified Crossbow Permit. This permit allows qualified people to hunt big or small game with a crossbow that has been specifically modified with a device that only allows it to be discharged (fired) by means of a breath tube. This permit does not allow the use of an unmodified crossbow