Prompong Nopparit submitted the plea to the Department of Special Investigation (DSI) on Wednesday, seeking the prosecution of Surachai Liangboonlertchai for breaking Section 113 of the Criminal Code.
The party said in addition to acting unconstitutionally, Mr Surachai accommodated the request of Suthep Thuagsuban, secretary of the People's Democratic Reform Committee (PDRC), who are on several arrest warrants.
Tarit Pengdit, DSI's chief, said the DSI had followed up on how Mr Surachai, who is also first Senate deputy speaker, had cooperated and accommodated Mr Suthep, who had been charged of 10 serious crimes.
Mr Tarit said he would forward the case to the police and the attorney general.
Mr Prompong said the Senate meeting in question had not been endorsed by a royal decree.
Besides Mr Suthep, Abhisit Vejjajiva, leader of the Democrat Party, was allowed to join the meeting.
The gathering discussed Mr Suthep's proposal, which centres around an appointed prime minister under Section 7 of the charter.
By allowing Mr Suthep to join the meeting, Mr Surachai should be charged with aiding and abetting, Mr Prompong said.