A sacked pastor is being held for allegedly slitting his wife's throat.
Kisii county police commander Jebel Munene said Joel Mogaka, 40, took the body of his wife Irene Nyakwara to the mortuary and said she took poison on Thursday night.
Police are questioning him.
"We have already begun investigations and already have credible clues," Munene said.
Nyakwara was a teacher at Bombaba Secondary School in Magena.
Her husband was sacked from the Seventh-day Adventist South Kenya Conference several years ago and ventured into farming.
Neighbours at Omosasa in Bomachoge Borabu told journalists they quarrelled often.
They said on Thursday night they quarreled about SMSs from another man on her phone, which led to a physical fight.
"There had been accusations and counter-accusations of infidelity. Elders tried in vain to iron out the issue," Tim Kironchi said.
The SMSs were allegedly sent by a police officer. The phone was confiscated
Police said they are investigating whether Mokaya had accomplices.
Police found blood spots in the couple's maize store and a bloody cloth.
The body is at Christamarriane Catholic Mission Mortuary in Kisii, awaiting postmortem.
(Edited by V. Graham)