Detectives are investigating reports of homophobic graffiti at a school which is at the centre of a row over lessons about same-sex relationships.
West Midlands Police said the vandalism on the school premises of Parkfield Community School in Birmingham was reported by a school governor during half-term.
The force also said it was reviewing video footage circulating on social media to “establish whether any additional offences have taken place”.
Footage posted to Twitter this week appeared to show a protest against the school’s “No Outsiders” initiative – which included lessons on LGBT relationships – outside the school.
A West Midlands Police spokeswoman said: “Parents have gathered outside Parkfield Community School exercising their right to protest peacefully on a number of occasions.
“Officers have been working closely with the school, the local community and the parents to facilitate the protests, and prevent a breach of the peace.
“No formal complaints have been made to West Midlands Police by Parkfield Community School or any of the staff who teach there.”
In footage posted on social media, young children appear to be joining in chants of “shame” while adults use the megaphone to voice their opposition.
In one video, a man standing on the back of a flatbed truck covered in banners saying “our children, our choice”, and “Stop! No Outsiders” says the programme is not just about teaching that other lifestyles exists.
He adds: “It is aggressively promoting them, giving it a positive spin, and telling people that it is okay for you to be Muslim and for you to be gay.”
The school is currently taking a planned break from the inclusiveness and diversity classes, which will resume after Easter.
Some parents, Christian and Muslim, have chosen to withdraw their children from classes. They claim the lessons, set up by assistant headteacher Andrew Moffat, promote his personal beliefs.
Ezra Stripe, a spokeswoman for charity Hidayah which provides support and welfare for LGBT members of the Muslim community, said the opposition to the programme was coming from a sense of “misplaced Muslim pride”.
She said: “It is depressing that we are still at this point today and it makes me aware of all the struggle our community has, in particular about isolation and shame and confusion.
“All this is just going to be duplicated in the next generation if we don’t start teaching this stuff.
“It is a conservative viewpoint that homosexuality is forbidden.”
She added the No Outsiders programme is simply trying to teach that some children may have two mothers and that it does not go into the intricacies of the relationships.
Last month, Ofsted Chief Inspector Amanda Spielman backed Moffat, who has made the final of the Global Teacher Prize for his efforts to teach diversity.
Moffat also runs a Parkfield Ambassadors after-school club that creates opportunities for children at his school – where 99% of students are Muslim – to meet people from different races, religions and cultures around Birmingham.
He left another Birmingham school following a similar dispute with Muslim and Christian parents.
Moffat, and the Parkfield school, have been approached for comment.
It follows criticism of the school’s local MP, Shabana Mahmood, after she appeared to support parents in their boycott of the relationship lessons.