Note that you don't have to (and should not) start a new message thread to post a question related to an earlier one. It is better to add a reply to the existing message thread.

If you think about your question, you should realize that no one is going to be able to answer it. There are 50 states in the US, each of which have their own record retention and sharing policies. How is anyone going to guess which state you are in and provide you with an informed answer?

Note however, that in some areas, law enforcement agencies have mutual information sharing agreements regarding applicants. If you fail to disclose your earlier application with a state agency, the local agency with which you are applying might find out anyway. In that case, your application might be rejected for lack of candor, regardless of what may be contained in your file with the state agency.

Why not call the agency with which you applied and ask how long they retain applicant records? (A period of several years would not be unusual.)