1:35 PM PT -- The store owners tell us Chris sent them a check on Monday for the full amount he owed them. And yes, this time they made sure the check cleared before informing prosecutors.

Chris Hansen is off the hook for allegedly bouncing checks -- which got him arrested in Connecticut -- because prosecutors dropped the charges ... TMZ has learned.

The former host of "To Catch a Predator" came up with the nearly $13,000 he owed to a mom-and-pop shop in Stamford, CT ... according to the court. As a result, prosecutors decided to drop the whole matter.

As we've reported ... Hansen was arrested and booked for larceny after allegedly bouncing 2 checks to the store owners.

Hansen’s attorney, Philip Russell, tells TMZ … Chris was in court Wednesday for a hearing, but he didn't have to plead to any charges after paying his debt in full.

As for when Hansen settled the tab, we'd assume he paid up after his arrest -- but when we posed that question to the court clerk we got a "no comment."