Muster and pay rolls of several militia regiments can be found in the National Archives and Records Administration microfilm series of Compiled Service Records. I've transcribed all the ones that are available and posted them on the Gerdes site.
Since the militia was a State organization, records of musters, officer appointments, etc., were supposed to be sent to office of the adjutant-general at Little Rock. Anthony Rushing has done a lot of work on this subject; he knows what records are available, and where they are archived.
Though not part of the State Militia, the records of Home Guard companies can be found in county court records (at least in those counties whose courthouses weren't burned down during the war).