Two people died of gunshot wounds in the western town of Siaya, and one from a head injury after falling over while running from tear gas in Kisumu, also in the west.
Police in Siaya opened fire "in self defence" after "a mob with catapults" approached a municipal office, according to a police statement, which said 29 officers were injured in the incident.
Riot police equipped with shields and batons used tear gas and water canon to disperse protesters who also tried to gather in the capital Nairobi and the port city of Mombasa.
CORD leader Raila Odinga believes the commission is biased, blaming it for his defeat by President Uhuru Kenyatta in the 2013 vote.
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The police statement also said prison wardens escorting criminals shot and injured five "rioters" who attacked their bus.
Opposition leaders claimed yesterday that several of their supporters had been "killed in various parts of the country" but gave no numbers.
"Innocent Kenyans have lost lives today," said Odinga. "We must condemn this in the strongest terms possible.