NYS - Need to file in probate court if my father ped away without a will, but held all property jointly?

My father ped away 6 months ago without filing a will. He and I held the house jointly (we live in New York city, Queens county, specifically), and all of his other accounts were held jointly with my mother. The mortgage and the car are probably the only things that are specifically in his name (and the mortgage may actually list me as a co-borrower - the bank and I are hashing that out). The mortgage was his only debt - do we still need to file in probate court? Or can I just file for a letter of administration? There's no disagreement among the heirs about who gets what (we all live together, and there's really nothing to distribute). Also, is there any sort of time limit as to when everything needs to get filed and done?