If you were never arrested there is nothing that would appear on a background check. Stop posting facts about what you might have done, as this is a public forum. And stop stealing.
All my comments here are intended for general legal purposes. None of my comments here establish an attorney-client relationship with anyone. None of my comments should be relied on in taking legal action without first consulting an attorney.
My colleagues are correct that you most likely do not have a criminal history record that will surface as a disqualifying factor in your effort for law enforcement employment. But that fact does not leave you with a navigable path to law enforcement employment, either. Most law enforcement agencies will conduct extensive pre-employment investigations including mandatory detailed disclosures by the applicant under penalty of perjury. The disclosures for law enforcement employment are not typically limited to convictions or even arrests but instead delve into all acts of dishonesty even where such acts did not lead to criminal justice system action. These interviews are generally done by skilled investigators who have spent their careers over decades interviewing criminals and suspects, and they are amazing at making credibility judgments. Law enforcement pre-employment investigations in many major jurisdictions frequently feature polygraph examinations, too. What's more, you very likely were entered into the retail theft data-base by either of the stores that you stole from, and law enforcement generally cross-checks against that data-base in its pre-employment investigations.
(1) Don't perjure yourself in any employment effort.
(2) Don't apply for work where a poly will be required.
(3) Work up a Plan B in case all of this theft catches up with you and defeats your plans for a career in law enforcement.
(4) Begin now with a determined and committed effort to be the kind of person that is eligible for law enforcement, or any other kind of career that interests you. Was whatever you stole worth being shut out of a meaningful career? Bet not. Get smarter on your own behalf. No one but you can save you from the consequences of terrible decisions.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.