Saroj Tharatin handed the petition to the National Council for Peace and Order at the army headquarters on Ratchadamnoen Avenue.
She was accompanied by Tossapol Kaewtima, a core leader of the People’s Army and Energy Reform Network (Paern).
Mr Tossapol accused police of trying to suggest Sutin was fired upon by both anti-and pro-election protesters.
He insisted Sutin was ambushed by “only one side”.
Sutin, 52, was shot dead and 10 other people injured on Jan 26 in clashes near Wat Sri Iam in the Bang Na area as protesters sought to block voters from entering a polling station for advance voting.
Sutin was a core leader of the People’s Democratic Force to Overthrow Thaksinism (Pefot), an ally of the People’s Democratic Reform Committee.
Pefot and Paern had earlier complained of a lack of progress in the police investigation into Sutin’s death despite the fact that video clips released on social media clearly showed a suspect.