The statute of limitation will depend on the type of debt and hospital debts and generally done under a contract for services, the forms you sign in the admission deparment will generally include the clause " I am responsable for payment" or words to that effect. This is a contract and contracts are enforceable for 10 years.

I have pasted a link to the statute below and the first five or six chapters is where you will want look,

http://apps.leg.wa.gov/rcw/default.aspx?cite=4....

Good Luck