It depends upon whether you owned the house as a joint tenant with your father or as a tenant in common. You tell that from the deed. If it was a joint tenancy, then upon your father's death you became the full owner. If it was a tenancy in common, your father's share must be probated. If you call, I will look up the deed and tell you which it is.
Attorney Meng is correct. If I were you, I would take him up on his kind offer. Good luck to you.
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I am licensed in Connecticut and New York and my answers are based upon the law in those jurisdictions. My answer to any specific question would likely be different if I were to review a client's file and have the opportunity to interview the client. Accordingly, I strongly urge you to retain an attorney in your jurisdiction with respect to any legal matter.