Police are investigating five allegations of malpractice relating to the Peterborough by-election, which Labour won by 683 votes.
Three of these relate to postal votes, one allegation is of bribery and corruption and the fifth is of a breach of the privacy of the vote, Cambridgeshire Police said.
Labour candidate Lisa Forbes was elected after the by-election on June 6, with Nigel Farage’s Brexit Party in second place.
Peterborough Council said on June 10 that it received one unconfirmed report regarding alleged bribery prior to polling day.
This was referred to police and no further action will be taken, the authority said.
In a statement, the council said that one other concern was received on polling day which was also referred to police, but could not be substantiated.
The council said it had seen no evidence that postal voting fraud had taken place.
Postal votes accounted for 9,898 of the 33,998 ballot papers received, and 400 of the postal votes returned were rejected due to either the signature or date of birth or both not matching council records.
The by-election was called after Peterborough’s previous MP Fiona Onasanya was forced out after she was jailed for lying about a speeding offence.
Onasanya was elected as a Labour MP in 2017 with a wafer-thin majority of 607, but was suspended from the party after she was sentenced.