She told reporters that she was being heavily trolled after her video was posted and she was extremely upset with it.
"If people are so angry with me, I would prefer to quit my job," she told reporters.
Her resignation, sent to Senior Superintendent of Police (SSP) Muniraj G., has not yet been accepted.
Constable Priyanka Mishra had apparently shot the video inside a police station and posted it on social media.
In the clip, posted a week ago, she is seen lip-syncing to a dialogue -- spoken by a male in Hindi -- that appears to laud what is described as Uttar Pradesh's culture of "rangbaazi (show-off)". The speaker seeks to compare the state's perceived notoriety with that of Punjab and Haryana, before suggesting that children as young as five years old have access to guns in the state.
"Haryana, Punjab toh bekaar hi badnaam hai. Aao kabhi Uttar Pradesh. Rangbaazi kya hoti hai hum tumhe batate hain naa gunday pe gaana banaate hain, naa gaadi pe Jat-Gujjar likhaate hain. Humare yahaan 5-5 saal ke launde katta chalaate hain (Haryana and Punjab unnecessarily have a bad name ... Come to UP. Neither do we glorify crime with songs, nor do we display our caste on our cars. In UP, kids as young as five know how to use guns)," the dialogue goes.
Priyanka Mishra, originally a resident of Kanpur, became a constable in the police department in 2020.