After learning from Murkrow in Chapter 1 that it was the one who Attacked the Aipom who had originallt stolen the little girl's Necklace, you will then learn from Murkrow itself that it doesn't have the necklace you are looking for. Because of this, you will then have to investigate further. Luckily, Murkrow will point you in the direction of Burmy, the same it had noticed earlier in the Park.
After finding the tree where the Burmy live, you will learn that another Burmy accidentally got caught up in the fight between Aipom and Murkrow. You will then learn from the trainer and its Scraggy playing soccer that their ball accidentally hit Burmy a little earlier, causing its leafy cloak to fall off. With this information, you must then go on the hunt for the missing Burmy, which just so happens to be found in the one tree in the Cafe Area.
After finding the Burmy in question, you will first have to Find hard evidence before being able to talk with it. In order to do this, talk with the elderly man in the Cafe Area to learn about Burmy, and then return back to the Fountain Area of the Park and question the boy who lost his pen the night before. From there, confirm that the Burmy in the first tree have said pen. Once this has been clarified, speak with the Park Caretaker from earlier to learn that some trash from the garbage can is missing.
After learning this, Tim and Pikachu will piece together that the Burmy that lost its first cloak must have used the trash in the area, including the Necklace, to create its new cloak. Return to the Burmy in the Cafe Area, showing the leaves from its first cloak in order to talk with it. After you do, you will Find the little girl's stolen necklace in this Burmy's trash cloak.