The incident happened around 11.50pm on Friday 1 March within the car park in Dryden Terrace.
A white Audi A1 was set alight and as a result, was completely destroyed.
Inquiries to identify those responsible are ongoing and anyone with information is asked to come forward.
Constable Matteo Margiotta from Dalkeith Police Station said: “This is a mindless act of destruction that has resulted in a car being completely written off.
“Anyone who saw any suspicious activity in the Dryden Terrace area on Friday evening, or who can help us identify the culprits should contact police immediately.”
Those with information can contact Dalkeith Police Station via 101 and quote incident number 5132 of 1st March. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.
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