Most states have pretty set rules.

In CT and NY, both states follow the Bowhunting mandate, "the first lethal shot". On that premise, what percentage of deer that are hit with a lethal shot are actually shot again, while bowhunting? Michigan and NY calculated some rough percentages when they initiated the NBEF program. Reports from states in the 1960's & 70's indicated that less than 1% of deer harvested were ever shot twice, and even today I would bet the percentage is still 1-2%.

For gun, I believe all states stand by the "killing shot", i.e. the shot that drops the animal. I know that is the law in CT and NY.

Although the DEC/DEP/DNR typically do not see many squabbles with bowhunters, gunhunting problems of this nature are common. If you want to legally claim the deer, you had better put it down. Head/neck shots in certain parts of the country are popular for just that reason, as it's either a clean miss or a dead deer.