The case in question is chapters 172-175 of D.Gray Man
These chapters feature one of the most popular tropes (yours and mine), the phantom thief! This is mostly a wacky interlude adventure for the exorcists before returning to the main plot.
Alan and Kanda and crew arrive in Paris which is basically on the verge of chaos thanks to a phantom thief named G. The city is on a manhunt but the perpetrator keeps changing bodies so the jail is over capacity with probable (okay, totally improbable since this is mostly a comedy story) suspects.
Our thief of course is using the power of Innocence to aid him in his crime spree, which makes him of interest to The Black Order.
And then G leaves a message that his next robbery will be at the Louve.
The ensuing trap to capture G is really entertaining as Allen and Kanda are thwarted and G continues to body hop. But G is doing his stealing for a worthy cause despite all the ruckus.
After Timothy agrees to go with the exorcists, things in the comic actually get really violent and crazy but that is after the phantom thief part has ended.
Honestly, there isn’t much mystery-solving in these chapters. The answer is revealed to us by a side character in fact. I just couldn’t pass up talking about a phantom thief making an appearance!