Since the military coup of 22 May 2014, there has been no legislative committee with the power to oversee the armed forces. This is because the Coup Group voided the 2007 constitution which provided for a legislature that possessed parliamentary committees.
Prior to the coup, Thailand also had a Senate Committee which was supposed to monitor the military. Prior to the 2013 dissolution of the Lower House, Thailand did have a Lower House Committee which served this purpose of oversight (under the 2007 constitution). The Lower House Committee had only three members with a military background. Though this could be interpreted positively in that the Lower House Committee was less influenced by the military, on the other hand the civilian members had much less expertise on matters pertaining to the military. Their lack of specialist knowledge meant that the military could sometimes dodge oversight. Meanwhile in the Upper House, the Committee overseeing the military had 7 members (out of 12) with a military background. It could thus be observed that military influence tended to be higher in this Senate committee with the implication that there might be less critical scrutiny of the armed forces in that body than in the Lower House.
However, since the 2014 coup, there has been no elected legislature and thus no elected legislative committees. In August, 2014, a National Legislative Assembly (NLA) was appointed by the military junta in power. This NLA, under the 2014 interim constitution, has no been given no jurisdiction to monitor the military, and has no power to scrutinize the military budget, although it can see the non-secret portions of the budget.
Meanwhile, the National Security Agency remains under the purview of Thailand's prime minister, who also doubles as military junta leader. According to an anonymous interviewee, currently there is no independent oversight of Thailand's intelligence services outside of the military itself.