Read to the end for an important update on this story.
Police were called to Corsham Primary School in Wiltshire early on Thursday 10 December following reports that Santa had crashed his sleigh beside the building.
PC Les Fletcher and PCSOs Shaun Redmond and Toni Brown, from the Corsham Neighbourhood Policing team, say the reindeer are known to have run off being chased by Father Christmas.
They are asking pupils, teachers and residents to let the school know about any sightings.
Appeal by Wiltshire Police
PCSO Shaun Redmond has made a video appeal to the public. He said: "We've been called to Corsham Primary School Broadwood site this morning following as report overnight of a crash.
"It is understood Santa has crashed his sleigh into the school whilst training some new reindeer.
"The reindeer have made off into the local area being followed by Santa Claus himself.
"Anybody with any information, please contact the school and they'll pass it on to us. Thank you."
Lindsay Fry, headteacher at the school's Pound Pill site says, while the situation was very serious, "the students were full of joy, surprised and delighted" at the crash landing. Some of them suspect they might have heard something or seen a flash in the night.
She has issued the following statement: "I am sure you can imagine it was a shock to all of us to arrive at school this morning and discover there had been an incident overnight.
"A vehicle had crash landed into the school entrance, leaving debris and carrots in its wake.
"On closer inspection we realised it was a very special vehicle indeed: Father Christmas’ sleigh, and that there was evidence of hoof prints and boot prints.
"We immediately sought the support of local police who attended the scene, along with highly skilled detectives, who asked the school community about possible sightings on their arrival.
"In a letter from the man himself, we have learnt that apparently Father Christmas was doing a practice run with some young reindeer whilst double checking his route, ready for Christmas eve.
"Somehow the sleigh has crashed and the reindeer have run off in the melee, and are seeking cover in Corsham, it is believed.
"The school and the police are appealing to anyone who has noticed any clues or spots them to get in touch with the school immediately."
The statement continues: "In the meantime, Father Christmas has set up camp in the school, and has asked the children to help him in finding the reindeer. For example, by making maps of the town and giving ideas where they might hide, so that he will have a better idea where to look.
"We really hope that the reindeer are found safe and sound soon, so that they can return back to the North Pole to finish those all important preparations for the big day."
Update: 17 December 2020
The headteacher has informed ITV West Country that a local reindeer expert came to the rescue and was able to round up the last of the runaways.
Lindsay Fry says, "She found them hiding in the local park and rounded up the last two; knowing that the best place to bring them was to Corsham Primary.
"The children got to meet them and were able to share the facts they had learnt about reindeer, before they were rounded up for Santa to collect. As you can imagine, the children were delighted that they had been found and that they had got to see them before their return!"
It is always good to report a happy ending!