Glasgow council officials said there had been at least 10 allegations of electoral fraud, in which voters attempted to impersonate other voters.
Glasgow City Council said police had been called earlier today.
They said it related to possible cases of impersonation, where people pretend to be someone else, cast the vote, then the real person turned up to vote at a number of unidentified polling stations across the city.
A council spokesman said: "The poll clerk had gone to score off the name and it appears the person had already voted.
"We then contacted the police.who asked us to recover the ballot papers. We can do that quite easily because we know the number of the papers and which boxes.
"It's not likely to slow the count."
The spokesman added there was little further details expected to be made public as the matter was now with Police Scotland.
Stewart Hosie, SNP Treasury spokesman at Westminster, said it was "very sad that people feel the need to engage in any kind of impersonation".
He told Sky News: "I think that's a daft thing to do. The ballot papers have been identified, they will be taken away and fingerprinted, the police will do their job and I'm sure whoever has done it will be caught and sentenced.
"That's the correct procedure. It won't change the result but of course it shouldn't have happened, it is a silly, silly, thing for anyone to try to do."
Officials are to use gloves to handle the papers at the centre of the incident - which were stored after being removed from the count - and they will be handed over to police. An official explained that it was to prevent their fingerprints contaminating possible evidence.
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