Filing taxes for deceased dad???

My father died earlier this year and I am the beneficiary. I received life insurance and got a 401K that I closed out. I know life insurance is not taxable. My problem is I don't know if my father has filed taxes in the past or not. He lived in LA and had little to do with his family. I believe that he might also owe back child support in WA. Will that affect me?? How do I find out??