Good morning. It looks like you are in California and I don't know if there is a specific rule there governing timing of notification. Perhaps we have a reader who would like to speak to that state.
Here in Pennsylvania, as a title examiner, we check the Register of Wills for estates that impact the property we are insuring.
I would advise that you call the Register of Wills for your county or stop by the courthouse with the death certificate and last will and testament, if one exists. Most folks hire an attorney to guide them through the system, but some do not.
When the house is sold, the title insurance company will advise you on matters affecting the property with regard to the estate. Their job is to clear title to issue title insurance so at least those issues would be taken care of.
I'm sorry for the loss of your father. Take care and good luck.