Labour's Sue Shinnick took the baked goods to a sheltered housing complex before winning her seat in Stifford Clays.
But her hospitality backfired after someone reported her to police accusing her of 'treating' - which means an attempt to influence votes - and breaks electoral law.
Now Essex Police are investigating the accusation, which comes under section 114 of the Representation of the People Act 1983.
If found guilty she could be imprisoned for up to a year and/ or face a fine.
'A person is guilty of treating if either before, during or after an election they directly or indirectly give or provide any food, drink, entertainment or provision to corruptly influence any voter to vote or refrain from voting,' the Electoral Commission says.
'Treating requires a corrupt intent – it does not apply to ordinary hospitality.'
A housing complex spokesman said: 'Cllr Shinnick bought cakes and sandwiches. It wasn't a grand buffet,' the Sun reported.