Locate your father's financial records such as statements from banks, stock brokerage statements, bank books, insurance policies, will if any, tax returns and bring them to an attorney to review. If you know your father's attorney that would also be a good source of information. Good luck.
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I agree that finding his attorney would be a good place to start. It doesn't sound like a will was probated but you could check with the county where he died to determine if his will was probated there or not. Reviewing his financial records and contacting those institutions might be a good place to look as well - especially if you are possibly a beneficiary of a life insurance policy, etc. It may also be that your mother is entitled to funds that were never taken so you can help her with that as well.
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I also concur with the other attorney's above, I think that either finding his Attorney or his financial records is a good start. I would also look to your mother, while she may not be coherent, her financial records, or papers are a good place to see if some money was left to her, which is going to pass to you, or if there might be a life policy on her life, I would call the same company and inquire about your father. Generally, my experience is that husbands and wives tend to have policy's with the same company, so it is worth a shot.
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