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I'm sorry to hear about your situation. Per your questions:
Can I ask employee to contact customer in an effort to recover my laptop? - Yes, you can certainly ask this. Now it is more likely that the dealership will give this information to the police, but you should certainly request it from the dealership yourself. If they say no, tell them that you are requesting a "litigation hold" on the surveillance tapes and any other evidence as to the identity of the individuals that took the laptop. This is something that will hopefully allow your attorney to request it in a lawsuit to ascertain the identity of the persons responsible for taking the laptop.
Or do I file stolen property police report solely? - It's not an either/or situation. You should do everything that you can to try to recover the property. This includes filing a police report, but also trying to get the dealership to work with you in tracking down the individuals that took it and seeking a quick resolution to the matter.
Is this a civil case or criminal? - Both, really. It's absolutely civil, as they took something that was yours without permission. That's called "conversion". If it was done with a "criminal intent" (that is, they had good reason to believe that it wasn't theirs and they took it with the intent to take possession of it (as opposed to returning it to you) then that's a crime. There can be criminal charges as well as a civil case filed for the return of the laptop or damages incurred (if they sold it on, etc...)
Is dealership responsible for wrong doing? - Most likely not. If they had taken possession of it (to a back room, etc...) and then through negligence it was stolen, you could have a better case against the dealership. But they have no obligation to exercise control over property that is left by customers, and the failure to do so (even if it results in the item being stolen) won't make them liable for those damages.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!