Police are investigating five allegations of malpractice relating to a by-election won by Labour in Peterborough earlier this month.
Lisa Forbes was elected as the city's MP after the former Labour incumbent Fiona Onasanya was forced out after being jailed for lying about speeding.
Cambridgeshire Police said it was looking into allegations including bribery and postal vote issues.
Peterborough City Council said it was standard practice to report concerns.
Earlier this month the council said it had received two reports of concerns relating to the 6 June by-election, and both had been referred to police.
No further action was taken regarding one, and the other could not be substantiated.
However, police are investigating three reports relating to postal votes, one allegation of bribery and corruption and one of a breach of the privacy of the vote.
Postal votes accounted for 9,898 of the 33,998 ballot papers received.
Four hundred of the postal votes returned were rejected due to either the signature or date of birth - or both - not matching council records.
Labour's Lisa Forbes won the by-election by 683 votes, beating Nigel Farage's Brexit Party in second place.
A spokeswoman for Peterborough City Council said: "Peterborough has a national reputation for its work to deter electoral fraud at elections which has been recognised by the Electoral Commission and other national bodies.
"We always refer all allegations of electoral malpractice to the police for investigation."