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They're not automatically responsible. The laws on "inkeeper's liability" are extremely confusing and convoluted.
One big issue will be whether there was a notice posted limiting their liability. We have stayed at a lot of LaQuinta hotels since they allow pets and usually they have a notice at the front desk, one on the check in slip, one on the desk in the room (or on the dresser or in the bathroom) and one or two more scattered around and in the elevator.
These notices can be sufficient for them to escape liability in certain circumstances. In addition, they can also blame the third party (the thief) and escape liability in that way sometimes.
Finally, they can try and evade liability by blaming you, claiming that you must not have closed your door completely, etc.
So, in essence, you have to be prepared to file a lawsuit and prepare for their defenses.