“That’s right, I did it,” a psychotic homeless man taunted cops after randomly clubbing a Midtown pedestrian in the head with a nail-studded two-by-four last November.

“I’m guilty — lock me up,” Andre Lineaux told officers according to statements he made to police released yesterday as he pleaded not guilty to an attempted-murder charge in Manhattan Supreme Court.

Lineaux admits he struck Kim Chong, 74 — a stranger to him — on East 40th Street at Madison Avenue in the unprovoked early- evening attack, but will argue at trial that he is not responsible because he is mentally ill, according to his lawyer.

Lineaux additionally pleaded not guilty to new charges that he had attacked and tried to pull a gun from a court officer during an appearance Nov. 13 in Manhattan Criminal Court.