I got chrged for theft 4yrs ago but was never convicted,I never even went to court and the case was dismissed-will it be on my record(background check)

Why was the case dismissed, did you pay a fine, serve time, anything?

No I did not pay a fine or serve any sentence-they said it was dismiss without prejudice because the info available was not sufficient to determine that the crime occurred beyound a reasonable doubt

Well then no, it won't show. You were only accused of something, they never convicted you of it.

So can that deny me from becoming a US permanent resident?

It will show up, but you can get it expunged. And most government agencies will not hold it against you. But allot of employers will, (some states have laws against this) in most states this is legal. But I would assume that you would be OK for citizenship. Good luck.

So what is the staus of limitation on a case like mine