The MP said that he had not received the summon and brushed it off saying the Sunday incident was political.
Police have asked MP Peter Kaluma and businessman Washington Ogaga to present themselves to Homa Bay Police Station within 44 hours or risk arrest.
The two rivals were involved in a scuffle at a rally in Homa Bay stadium on Sunday.
County Police Commandant John Omusanga and Criminal Investigations Officer Michael Mugo accused the two politicians of breaching the law.
Mr Ogaga is seeking to unseat Mr Kaluma from the Homa Bay Town parliamentary seat in the next election.
Mr Omusanga said they have evidence that the two politicians had breached the law by fighting publicly and causing disturbance in a political rally addressed by Cord leader Raila Odinga in Homa Bay Town on Sunday.
“We investigated the matter and concluded that the two politicians should record statements immediately with the police or they be arrested,” said Mr Omusanga.
He argued that he is the one who was beaten and therefore does not need to record any statements.
“I am not going to record any statements with police because this issue is political,” said Mr Kaluma.
“We will take the two politicians to court for breaking the law,” said Mr Mugo.
Speaking to Nation on phone, Mr Ogaga said that he requested the police officers to allow him record statements at the nearest police station but his request was declined.
“I have to travel all the way to Homa Bay Police Station to record a statement,” said Mr Ogaga.