Game is considered state property. F&G is responsible for collecting road-kill and if it has any value (like fur) they have to preserve it for sale or useful disposal. If you can reach an F&G officer promptly to report the incident they will probably allow you to keep your road-kill. Make sure you note who you spoke with since it is technically poaching to possess game that was not legally taken.
Or... Toss in in your trunk and hope no one saw you!
(There's nothing like freshly grilled game!
)