Well, even if you could, don’t do it! Do not move the carcass around at all, just take the meat. Very important!
Thinking back, I now remember how it went down. I read the regs and didn’t find anything in regards to gifting. So I stopped by the FW and asked. I was told that the permit is required, so I would need to provide the animals I am gifting, the year they were harvested (they said they would fill in the tags themselves), the name(s) and address of the person accepting the gift, the address of the place where the meat is going, the weight of the meat from each animal (not the total from all), the hunter’s win number, and $21 in cash (at least used to be the only method of payment where I got the permit). I even included, but didn’t have to, half a dozen or so of bunnies I snared and gave away to avoid any questions if the situation arose, lol.
Edit: here is what the meat portion looks like on the permit (I gave away the left over deer from the previous year and about half of the cow elk I shot that year, along with 3 kg of rabbit, haha):