I dont record city park finds as they have little educational value. In the boonies i looks for other than coin objects out of place. Those you may wish to get photos during the dig, a measurement of how deep, a compass heading via a compass placed near the hole with a picture. You also may wish to have a few phone numbers or emails ready if you should make a major find. While most of us would never turn in our old bullets and belt buckles to a qualified archy.
So if you find bones, ancient pottery, crystal skulls that give you majical powers. It is best to take photos of measurements, gps, and place back in hole and turn over to local universty or state archy. Bones also require you notify the police.
Hope this helps. Laws and rules vary by state depending on fed, state, blm, and even private propoerty. You also have National Forrest and Reservation, to include Preserves that prohibit digging any digging at all. Now I have really just confused you, relax. Use common sense, dont be afraid to talk with a park ranger, or care taker. The fines and penaltys can be stiff, but knowing what you need to document and where is very important. Sorry if I went a little in depth here. No one told me all this when I started, I found out the hard way.