The answer is covered amply in the screenplay.
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Major Strasser has no official powers in Casablanca.
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Captain Renaud is willing to cooperate with the Germans. He is also willing to arrest Lazlo – if Lazlo breaks the law. Since Casablanca is independent of Nazi Germany, though, Renaud has to be able to charge Lazlo with something.
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When Strasser tells him to shut down Rick’s (note – it’s not technically an order), Renaud is willing to go along because he does have a reason and because he wants to cooperate. Shutting it down is also within his powers, whereas arresting Lazlo would only put Lazlo in front of a judge who could release him.
An interesting point – if Strasser had bribed Renaud to arrest Lazlo, it probably would have happened.
“What we have here is failure to communicate.” – Strother Martin, anticipating the Internet.