It is thought that youths started a fire at the unoccupied building, on the night of February 25.
The fierce blaze, Scarborough’s biggest for many years, was tackled through the night by firefighters.
Eastfield residents helped to identify suspects when they posted a photograph of a group of teenagers on the grounds shortly before it began on a community Facebook page.
Three boys have been arrested on suspicion of arson, and inquiries continue.
If you can help with the inquiries, any photos, video or ring doorbell footage should be passed to North Yorkshire Police via email to cidscarborough&[email protected], or you can call 101, select option 1, and speak to the Force Control Room.
Alternatively, contact Crimestoppers anonymously on 0800 555111.
Quote police reference number 12220033765 when providing details.
The old school site became vacant following the completion of the development of the new Overdale School site at Middle Deepdale last year.
Residents and councillors had hoped that the old school could be used for community use.
A spokesperson for North Yorkshire County Council said: “The county council will require to obtain the consent of the Secretary of State for Education to utilise the site for any purpose other than education within the next eight years.”
Jon Holden, Head of Property Services at the county council, said: “We were considering future uses of the existing buildings and site, including in consultation with local stakeholders.
"Unfortunately, the recent fire caused extensive damage so we are further reviewing the action that is required as a result. We hope to be able to make a decision shortly."