When James Corden's character investigates the stolen necklace, why was Tammy not questioned? Especially since she's the one who "pulled it from the water".
As an experienced investigator, John Frazier (Corden) was quick to identify his real lead. It is true that he probably should have started with Tammy as you say, coz after all she is the one who pulled it out of the water. But he realizes that Tammy is not the big fish.
He already has his own doubts and his eyes on Debbie. He possibly even knows that Tammy is a known associate of Debbie and Lou's. Given this, why would he waste his time on Tammy only for her to deny any involvement in this. The crew certainly would have prepared for any initial investigation against her. That is why you see the one with the cleanest background infiltrate Vogue. Tangling with her would have cost Frazier precious time. Time he wanted to spend getting back the necklace.