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..."You have to answer verbally and the soldier marks the answer on the sheet and keeps it," one woman in Enerhodar told the BBC.
In southern Kherson, Russian guardsmen stood with a ballot box in the middle of the city to collect people's votes.
The door-to-door voting is for "security", Russian state media says.
"In-person voting will take place exclusively on 27 September," Tass reported. "On the other days, voting will be organised in communities and in a door-to-door manner."
One woman in Melitopol told the BBC that two local "collaborators" arrived with two Russian soldiers at her parents' flat, to give them a ballot to sign.
"My dad put 'no' [to joining Russia]," the woman said. "My mum stood nearby, and asked what would happen for putting 'no'. They said, 'Nothing'.
"Mum is now worried that the Russians will persecute them."
The woman also said there was one ballot for the entire household, rather than per person.
Although the evidence is anecdotal, the presence of armed men conducting the vote contradicts Moscow's insistence that this is a free or fair process.
What Russia wants from the votes in occupied Ukraine
Experts say the self-styled referendums, taking place across five days, will allow Russia to claim - illegally - four occupied or partially-occupied regions of Ukraine as their own.
In other words, a false vote on annexation, seven months into Russia's invasion.
The self-styled "annexation" could lead to Russia claiming that its territory is under attack from Western weapons supplied to Ukraine, which could escalate the war further....