There is no hard and fast rule for you to apply at any Muroor. But none of the Muroor will entertain people from other governorates. The answer probably will be that they already have enough work load. If you already have a file at any of the governorates previously then you will have to go to those even if you are residing anywhere in Kuwait. Example, for Renewal of Licenses or me having a 4 wheeler license and wanting to gain a 2 wheeler license.
Hope someone might give a better insight and be of help to the questioner.