Good morning. If your father died without a will...and I'm presuming now that you and your brother are the only children and that there is no surviving spouse and neither of your father's parents is alive, then under CT's intestate succession laws, you and your brother inherit this house (and it's contents) in equal shares. One of you will need to petition the probate court to be appointed the executor of your father's estate so that person has the authority to transfer ownership of the house to the two of you.
Now, because you have lived there for years, you would be considered a month to month tenant. As such, after someone has been appointed executor, that someone can terminate your tenancy with a 3 day notice. So, it's important that you petition the court to be the executor. Because then you can stay until the property is distributed.
I hope this has given you the guidance you were seeking. I wish you the best of luck!
If you have a follow-up question, please remember that there might be a delay between your follow up questions and my answers because I may be helping other clients or taking a break.
The information given here is not legal advice. As all states have different intricacies in their laws, the information given is general only. This communication does not establish an attorney-client relationship with you. I hope this answer has been helpful to you.