I'd at least expect them to speak to the hotel and let them know they're involved.
That way, if a staff member had stolen it, and knows that the police are sniffing around, they would likely be frightened enough to 'find' the lost item before it gets more serious.
If it was supposedly not missed by 'friend' until after they'd vacated, people almost always pull the door to when they leave, so it automatically locks. Thus only a staff member would have had a key to get in before the next guests arrived.
A cleaner would be extremely familiar with the usual contents of the room, so a fancy hair dryer that they don't supply as standard - especially one still in its box and on the floor, behind the door, would stick out like a sore thumb to them.
An honest cleaner would thus alert the manager and hand it in, so it could be kept safe and reunited with its owner when they call to ask if it's been found (or indeed if the hotel contacts them as soon as it's found).
Thus it would have been found and removed from the room long before any further guests had chance to find and steal it - so no need for the police to contact them at all.