PA 22-135 Pilot reported an inability to climb during takeoff resulted in an off airport landing. The aircraft was recovered for inspection.

Narrative

Upon proper run up and leaning for an altitude take off aircraft failed to climb after rotation. Engine was running and no misses; flaps at 2nd position and a climb altitude was established. Using Runway XX; take off appeared normal approximately half way down Runway XX. Upon lift off the aircraft failed to increase in airspeed and to sink. An attempt to turn off runway heading to slightly descending terrain did not help. Upon stall speed this writer made the decision to make an off airport landing. Upon a hard touch down the aircraft rolled out under pilot control to a safe stop. The aircraft did not suffer any prop strike. No other property damage occurred or personal injury. Upon recovery by tow truck to the Hanger at ZZZ it was noted that the wing tanks fuel was leaking; some minor under belly scraps on the tail section and a very slight bump on the rudder had occurred from the hard landing. Also noted were some under belly inspection panels that had been bent slightly from an over active landing gear travel. The final issue was a slight rear passenger door frame bent outward and on its reverse side a small half inch crack. Once the aircraft was parked in the hanger the leaking fuel stopped. The engine was started and warmed up and the mag checks; engine temps and operation were normal. On full run up and leaning the tachometer showed approximately 2400 RPM which is normal for other airports this aircraft has successfully taken off from.