What happens if you steal and store doesn't call to policy?

My wife and my baby girl (3 years old) were shopping today. My wife didn't pay attention and baby girl put some toys, some clothing with XXL size in the stroller (total of 75 $ they said). They caught them when they are leaving the store. Since my wife didn't have ID and she gave them my cell, they called me and I went there. They couldn't show how my wife was taking items and it was obvious that if one wants to steal something, he/she won't steal this kind of craps... all toys and crappy stuff. They didn't call to police. They asked my wife to sign some papers (so she cannot come to the store in future). Since my wife didn't have ID, they photo copied my ID and kept, and said they will send some fees (I offered to pay in the store, but they said they will send a bill). I am worrying about this....Can/will they file any my criminal record for me or for my wife?