It probably followed the deer into town as they go where the prey goes.
I personally am glad you did not shoot it but I would understand if you did especially if you have small children. So long as it is a healthy cat and there is
no shortage of it's natural prey you really have very little to worry about. It is either younger or old sick ones that usually attack humans usually either kids or small women. It pisses me off that I live where we have wolves ,bears ,cougars ,lynx etc but no one is allowed firearms in their vehicles or on their person unless legally hunting or on the way to or from the range(no you can't make any stops). If you were a Canadian you would have had to hit it with your prosthetic leg.