My DAD renewed his lease which went into effect on April 1, 2008. He passed away on May 10, 2008. I lived with him and was listed on the lease as "occupant". Due to his untimely death, I am no longer able to stay. I spoke with the Property Manager and explained situation to her, and wrote a letter stating that I could no longer afford to live at said property, and would be vacating the premises by June 30, 2008.( I was able to pay the rent for the month of June, 2008).

What I need to know is "what if anything am I legally responsible for" as far as breaking the lease?":

If you actually signed the lease, you are responsible for the entire term.

If you didn't sign, you are not responsible for any of it.