There have been calls to press criminal charges against Mr N'gondi.
Kenya's Association of Muslim Lawyers says a politician who appeared to force a woman to shake his hand should be investigated for harassment.
A widely circulated video of an office birthday party shows Ken N'gondi, the Speaker of Nairobi's County Assembly, apparently insisting that a female Muslim colleague shake his hand. He is also seen putting his hand on her shoulder when she stands up.
Mr N'gondi has not commented on the video.
News outlets and social media commenters point out that devoutly Muslim women do not shake hands with male acquaintances.
Many say the woman in the video looks uncomfortable, and Muslim lawyers have said it amounts to sexual and physical assault.
They say they're demanding "accountability" for what happened and want police to bring "criminal charges" against Mr N'gondi.
