I would say that from your description of the cat; no front claws, healthy looking and friendly that it probably belongs to, or did belong to someone in the vicinity. If it doesn't pose a problem, and isn't a nuisance or a threat, I would let it be. This time of year homeless animals, even in urban areas, tend to look fairly unkempt because of the places they have to use for shelter are generally abandoned and/or pretty dirty. If you're worried about the cat's health or well-being, call a shelter and ask for their opinion.
