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All 50 states have dog licensing in some form, but it seems that it's more a case of the state allowing municipalities to do so or not. Some states also require veterinarians to report unlicensed dogs. Larger cities almost certainly require it (NYC and Chicago definitely do).

https://www.rover.com/blog/dog-license/

Usually it's an animal welfare and control thing: you pay a lot more if you don't spay/neuter, rabies vaccination is required, etc.. Otherwise it's too easy for a city to be overrun by strays.

Also, if your pet gets lost and ends up being picked up by animal control, it's considered a stray if it's not registered.