You will have to apply with the Probate Court to be the Administrator of the estate. You will have to advertise for 4 weeks in the local paper to be named Administrator. After the four weeks the Probate judge will confirm you as administrator after a two week period beyond the advertisement ends. This is if no one contest you being named. Then You have to advertise as the Administrator in the local paper to all debtors and creditors to the estate. Once that is satisfied then division of assets will be made following the law governing intestate succession.
If you can't get your Dad to get a will, in my opinion for what it is worth get an attorney to help you with establishing an estate. You are going to want all the t's crossed and I's dotted.
I am not an attorney, just speaking from experience.
What you said is about how I was thinking it would work.
I have learned that the CD is payable on death to me and my sister.
I am a signer on his checking but unsure if I could use it after death.
My sister is joint owner on his savings and house.
We'll figure it out and maybe it won't be too painful of a process. This is all new to me.