Since you tagged your post under the "Collections" Tag, I presume that you have obtained a Judgment in one state and wish to enforce that Judgment against the Debtor in another state. The answer is that this is possible under Full Faith and Credit principals but does take some work.
In most cases, you need to obtain a certified or exemplified copy of the Judgment from State 1 and bring and file an Application to domesticate that Judgment in State 2. "Domestication" just means a request to have State 2 recognize and enforce the Judgment from State 1. You have to do your own legwork as the Courts will not do it for you (except in certain circumstances such as child support). Obviously the easiest thing to do is to hire counsel in State 2 to domesticate your Judgment for you and to pursue collection of the Judgment.
Answered on Oct 11th, 2012 at 1:14 PM