Green’s Dictionary of Slang

to play a practical joke based on one’s pretending to be mad, esp. to have just escaped from one’s keeper or from a psychiatric institution.

1785

Grose Classical Dict. of the Vulgar Tongue n.p.: Dowdying, a local joke formerly practised at Salisbury, on large companies, or persons boasting of their courage. It was performed by one Pearce, who had the knack of personating madness, and who by the direction of some of the company, would burst into a a [sic] room, in a most furious manner, as if just broke loose from his keeper, to the great terror of those not in the secret. Dowdying became so much the fashion of the place, that it was exhibited before His Royal Highness the prince of wales [...] Pearce obtained the name of Dowdy, from a song he used to sing, which had for burthen the words dow de dow.