Kent police have invited schoolchildren aged 13 and 14 to write an essay on their feelings about homosexuality.
The force has organised the competition as part of lesbian, gay, bisexual and transgender (LGBT) history month.
It offers a £25 book token as a prize for the best essay under the title “All Different, Same Respect”, the force’s slogan for a series of events marking the history month.
Ann Widdecombe MP, whose constituency is in Kent, said: “I would have thought the police had other things to worry about, like catching burglars.”
Other police gestures to mark the celebrations have been dismissed by critics as “political tokenism”.
Last week a senior police officer signalled the neutrality of his force on political issues by ordering the removal of a rainbow flag from a London police station.
The rainbow flag is the chosen symbol of the ‘gay rights’ movement, and was flown at the police building to mark LGBT history month.
Commissioner Sir Paul Stevenson ordered the removal of the rainbow flag because only the Union Jack and the Metropolitan Police’s own flag are to be flown from police buildings.
The move was reportedly intended as a sign that the London police force will not “stray into political territory”.
The flag has been flown at other police stations around the country.
One MP in North Wales questioned the decision to fly the flag at the police headquarters there.
David Jones, MP for Clwyd West, told The Daily Telegraph: “I can’t see any reason why any flag other than the Union Flag and the Red Dragon of Wales should fly outside our police headquarters.
“This is tokenism and posturing. People want to see their police force focus on fighting crime, not getting involved in political tokenism and gestures.”