Officers were called to Willowbank Nursing Home in Pasturegate shortly after 5am on Tuesday (August 17).
The man, who was reportedly wearing women's underwear and a clown mask, was caught performing a sex act on himself after standing at a window.
Police quickly flooded the area after members of staff raised the alarm, but the man had already fled the scene.
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Det Insp Mark Saunders, of Burnley CID, said: "This was an extremely distressing incident and we are doing all we can to identify and arrest the offender.
"Even if you think that a piece of information isn't significant I would urge you to contact us so that we can review it alongside other intelligence and information we have."
"I appreciate that the nature of this incident may cause concern in the community and I would reassure people that we are doing all we can to identify and apprehend the person responsible."
Anyone with information has been urged to contact police on 101, quoting log number 0194 of August 17.
You can also report it online at the Lancashire Police website by clicking HERE.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555111 or online at crimestoppers-uk.org.
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