Chadema said on X that one of its candidates, Modestus Timbisimilwa, was beaten to death by police in the commercial capital Dar es Salaam as he attempted to stop "fake ballots being inserted into ballot boxes".
It said another candidate, George Juma Mohamed, was shot dead by police at his home in Mkese in central Tanzania the night before, according to the party.
Police said in a statement that the death occurred after a group of prison officers were called in to deal with a clash between supporters of Chadema and the ruling Chama Cha Mapinduzi (CCM) party, and fired "warning shots".
Another Chadema official, Steven Chalamila, was killed in a machete attack at his home in Tunduma near the border with Zambia, also late on Tuesday, according to the party.
The ruling CCM party has been accused of increased repression of the opposition in the run-up to the vote.
"We condemn the murders that have occurred and demand that the police take immediate action to arrest and bring all perpetrators to justice," Chadema said in a statement.
Wednesday's ballots are a key test for the parties and the country's democratic institutions ahead of a presidential election next October.
Tanzania is electing more than 80,000 local leaders, who wield considerable power in the East African nation.
'Pre-marked ballots'
Chadema says many of its candidates were unfairly disqualified and had already listed claims of multiple irregularities before polls closed on Wednesday.
It said its agents had found pre-marked ballots for ruling CCM party candidates in several locations, but were arrested by police when they tried to intervene.
An AFP journalist in the western city of Kigoma saw voters clashing over alleged fake ballots, leading to arrests.
"We demand that TAMISEMI (the local government ministry) provide an explanation to the public regarding the pre-marked ballots for CCM candidates in various parts of the country," Chadema said.
The ruling CCM of President Samia Suluhu Hassan, a dominant force for decades, is facing a strong challenge from Chadema which boycotted the polls in 2019 citing violence and intimidation.
"We are electing local leaders who are also important campaigners during the general election," Chadema's director of communication and foreign affairs John Mrema told AFP on Tuesday.
Hassan took office after the sudden death of her authoritarian predecessor John Magufuli in 2021.
She was initially feted for easing restrictions that Magufuli had imposed on the opposition and the media in the country of around 67 million people.
But rights groups and Western governments have criticised what they see as renewed repression ahead of the elections, with opposition politicians facing frequent arrests, as well as abductions and murder.
In 2019, the opposition boycott paved the way for a clean sweep of the seats by CCM.
