generally, your dad will have to sign the release over to the dealership where you trade it in. The title owner has to sign the dealerships release forms.
These dmv laws differ from state to state, therefore, you need to contact the dealership where you plan to trade it in and be guided by what they tell you and get that persons name. Dealerships have specific people that only do titles/regs.
People here really can't give any info unless they do this all the time in that state. There are too many differences in the DMV laws between states.