Assuming your father died in Florida, you can open up an estate at the local courthouse. Is your mother alive? Was he married to anybody else at the time of his death? If nobody has a superior right to administer his estate, then you can get appointed as the personal representative of the estate. If he died with few assets, you may be able to file a Petition for Summary Administration, which is relatively simple. You will need to file the petition at the courthouse, along with a death certificate and an order for the judge to sign. If the estate is somewhat larger or requires administration, you'll need to file a formal petition for administration, and apply for letters of administration. This process is more complicated, and you should probably get a lawyer for it. (Feel free to contact me, if you wish). Once you are appointed as the personal representative by the estate, you can close your father's bank account and withdraw the funds (But be careful. You should probably re-deposit those funds in an estate account, until you can appropriately settle his affairs, clear his taxes, etc). Good luck.
You can seek the assistance of the Small Estates Dept. in the Miami Dade Probate Court. They can assist you in obtaining a court order for releasing the funds in the bank account if your situation warrants it. These questions are quoted from the FAQ in the Probate section of the Miami Dade Court system:
What do I need to obtain a court order so that the money in a bank account belonging to my deceased husband can be released to me?
First of all, the account must be the decedent's entire estate. If you are the one who has paid the funeral bill, then we need a copy of the paid in full funeral bill, a copy of the death certificate and full information concerning the asset in question. If you are not the one who has paid the funeral bill, then we need that person's consent in writing.
Why do I need a copy of the paid in full funeral bill?
Because the purpose of the Small Estates department is to reimburse the person who has paid the funeral bill.