Car owner gets first Dibs, then they can give it to whomever they want.
Went through that shit here about 20 years ago, guys Wife hit a MONSTER Buck, Deputy and State Patrolman asked if her Husband would want it, she said she didn't know but he would be there.
The Authorities called someone and he came out and got the Buck, Husband shows up and raises holy hell and Deputy said he should have got there sooner and Husband flips out.
Deputy says if Husband don't calm down he will arrest him for disorderly, well Tow Truck arrives and Husband & Wife head home, next day Husband calls Sheriff, raises hell and Sheriff said Patrolman issued the Temp Permit.
Guy calls State Patrol Barracks and talks to Commander, Commander says he will get to the bottom of it, well the STatey says the Deputy called a buddy and told him to come get this huge Buck and the Deputy issued the Permit.
Sheriff found out and blew up on the Deputy and made the Deputies buddy take the deer to the rightful owner, that Buck Netted 197" and the Sheriff issued a new Temp Permit for the Antlers.
But a lot of times out here Women drivers tell the Deputy they don't want the deer and when it's a Big Buck the Deputy or a friend of the Deputy end up with the Buck and some Huge Bucks have been killed that way.

Not in my state......

That was in northern Harris County TX.  Houston area.  Huffsmith-Kohrville Road is also known as FM 2978.