Under electoral law, potential voters cannot be given incentives, including food, to encourage them to vote for a particular candidate.
But Ms Brabin has been pictured handing out brownies with supporters tweeting their thanks to the frontrunner in the race.
Complaints began after Liberal Democrat councillor for Knottingley and Ferrybridge Tom Gordon said he had twice seen Ms Brabin handing out boxes of brownies with “Vote Labour” written on them.
And the agent for Conservative candidate Matt Robinson has complained to West Yorkshire Police and the returning officer for the election.
Mr Robinson said: “This goes to show how desperate Labour are in West Yorkshire. This is now a matter for the police to investigate further. Meanwhile I’m concentrating on speaking with residents of West Yorkshire and about my pledges for boosting our region’s economy, delivering more police on the beat and connecting our public transport system.”
A Labour source said: “While Tracy has been talking to voters about her ambitious plans to sort out transport, back the police, create jobs and lead our recovery from the pandemic, it’s telling that the Tories and Lib Dems have resorted to wasting police time complaining about what cakes she offers party members after a hard day’s campaigning.”
A West Yorkshire Police spokesman later said: "West Yorkshire Police can confirm that after an investigation following the circulation of social media posts and a direct complaint re electoral matters that no offences have been recorded."
It is understood these were only available to Labour activists as a thank you for helping with campaigning.
Labour has also been criticised for multiple photos posted on social media showing campaigners in groups of more than six, despite coronavirus rules saying groups larger than this should not meet, even outdoors.
In one photo of campaigners in Pontefract over the weekend eight people, including Ms Brabin, were pictured.
Another in Wakefield showed seven people holding Labour leaflets.
Ryan Kett, who is standing for the Yorkshire Party in Pontefract North, said he had been alerted to the photos by a member of the public, who had also reported the alleged breaches to the police.
He said: “After perusing their local social media pages I noticed that this seemed to be a regular occurance with groups of up to nine.
“I don’t feel that it’s fair that members of the public should have to adhere to these clear guidelines or face a heavy fine whilst Labour candidates and activists are getting away with breaching the rules with impunity, they seem to believe they are above the law.”
He said he was concerned some of those photographed may be at election counts and added: “It concerns me that if Wakefield Labour don’t understand the need to comply with the rule of six they may not consider other guidelines important, such as the need for everybody at the count to carry out their own lateral flow test, and in some marginal seats in the Wakefield district we have to question whether Labour candidates are gaining a competitive advantage against those who are complying with the rules.”
Another photo has since emerged of Conservative campaigners, including Mr Robinson, seeming to break the rule of six.