If you suspect an employee has been stealing, you can and should discipline him. You don’t need absolute and irrefutable proof. It’s enough that you reasonably believed he stole.
Recent case: Lewis, who is black and over age 70, was fired from his job with a pallet company after managers received an anonymous call alleging he was stealing pallets. Since a truckload had gone missing, the company believed the caller.
Lewis sued, alleging age and race discrimination. The company countered that it genuinely believed he had stolen the pallets. That was enough for the court to throw out the case. (Stephens v. Neal’s Pallet Company, No. 3:11-CV-173, WD NC, 2012)
Final note: Make sure you have records to back up your belief. In a case like this, that might include notes taken right after the anonymous tip.