@najerace,
I don't believe dogs are like cars. You don't need a title to prove you own pet and dog's don't have VIN numbers like cars either.
When I moved to NYC and into the apartment with my friend Eurodiva, she had a husky for 4 years (at that time) and never registered the dog with the city.
I registered the dog but the city didn't need any other information other then contact information (address, phone,...) and rabies shot information. The form never asked for any other information and the city never called about where the dog came from, who previously owned it, or why it wasn't registered in the first place. They just want the licensing fee and the knowledge that you're obeying the rabies shot law.