It is not uncommon that deer hit by a car survive long enough to flee the scene and then succumb to internal or structural injuries.

How to dispose of the dead animal

There isn't anybody in state or local government who will come out to necropsy the deer. The deer isn't an immediate health hazard, but it will decompose and produce foul odors.

• Dispose of the animal as quickly as possible. The deer's gut is filling and pressurizing with decomposition gasses and matter, which will be released if the deer's organs get pierced and produce more unpleasant odors. The body will also attract both natural and domesticated scavengers.
• Wear protective equipment such as gloves, face masks, and eye protection in case of splatters. Be wary of ticks transferring from the animal to yourself. This article has more information on how to identify and avoid ticks: How to protect yourself from ticks, OSU Extension
• Roll the animal onto a sheet of plastic and then into a dumpster. Perhaps ask your garbage company if you could use the yard waste cart if that one is relatively larger.

In the future, keep in mind that when deer die on a public roadway, you can call the roads department (city, county, or state highways as appropriate) to clear dead animals' bodies.