No offences took place with three of the five allegations of malpractice at a by-election in Peterborough earlier this month, a police inquiry has found.
Labour won the seat after its incumbent MP Fiona Onasanya was forced out after being jailed for lying to police.
Police said no offences were revealed with one allegation of bribery and two relating to postal votes.
An allegation of breach of the privacy of the vote and one of the burning of ballots were still being investigated.
Lisa Forbes won by 683 votes in the 6 June by-election, with Nigel Farage's Brexit Party in second place.
A Cambridgeshire Police spokesperson said: "I can confirm police received several reports of electoral fraud following the Peterborough by-election.
"Of the five allegations reported, two incidents are currently being investigated to establish if any offences have been committed.
"No arrests have been made."
Peterborough Council said it received one report of alleged bribery prior to polling day, which was referred to police and resulted in no further action.
It said another concern was received on polling day which was also referred to the 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.
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 for lying about speeding earlier this year.