Perth's Lord Mayor Lisa Scaffidi has retained her position after local Government elections.

Ms Scaffidi defeated her only challenger, Anne Bontempo, by 1,222 votes.

The WA Electoral Commission counted just over 4,300 ballots in the Mayoral contest.

Before the vote count finished, Ms Bontempo said voters cannot have any faith in the election result because of allegations of vote rigging.

Police are investigating how six voting packages were stolen from the post boxes of a residential building in West Perth.

"We have no idea whether it was five votes, 500 or 5,000 votes that have been tampered with," Ms Contempo said.

"As well as the fraud squad investigation into this matter I would like to call on the Corruption and Crime Commission to investigate this issue.

"This is a very serious matter that undermines our democratic rights."