I have never heard of any city that holds a homeowner responsible for disposal of carcasses of animals hit on a city road that landed on their property.
I don't really know what will stop the stink. Around here any dead animal will be dispatched quickly by bald faced buzzards, hawks, eagles, coyotes, etc..
Count me as another person living where the county and city holds the homeowner responsible for disposal of carcasses of animals hit on city/county roads that landed near their property. A neighbor of ours (5 houses from us) had to deal with this and experienced the exact same problem. We're 50 min west of Wash DC and live in a suburb city. She complained enough to where they came and got it (there's NO other way it could've been dealt with - we live on postage stamp lots), but they argued the whole time that since the animal didn't drop in the middle of the street or shoulder, it wasn't their problem. The lady lives maybe 15-20' along the side of the highway, it clearly suffered a major impact with a car and the road is close enough to where a 7 yr old can throw a rock from the yard to the highway.