Judah Adunbi, 63, was hit in the face when officers mistook him for a wanted man in Easton, Bristol, on January 14.
A video of the incident appeared to show Mr Adunbi refusing to give Avon and Somerset Police his name, before a brief tussle with a male and female officer, and the discharge of the stun gun.
The Independent Police Complaints Commission (IPCC) said it has served the two officers with gross misconduct notices as part of their investigation which is “progressing well”.
A complaint from a member of the public who witnessed the aftermath of the incident was voluntarily referred to the IPCC by the force, it said.
IPCC Commissioner Cindy Butts said: “The incident in which Mr Adunbi was tasered has attracted significant community concern and I am grateful to the representatives for their attendance last week and their honest and frank contributions.
“We would reassure them that we are conducting a thorough investigation into the circumstances surrounding this incident.
“The investigation is making positive progress and we are continuing to review evidence regarding the appropriateness of taser use in the circumstances.”