I believe at least two were produced. Here is the write up from Ferrari:
365 P Speciale (1966)
In 1966, Pininfarina built a three-seater berlinetta over a V12 mid-engined sports-prototype chassis (4,390 cc, 380bhp). It created a huge furore. This once-off was built to order for Gianni Agnelli and was followed a year later by another special model for Luigi Chinetti. The 365 P Speciale boasted a more harmonious version of the lines of the Dino prototype. The headlights were faired in and the roof was made from Plexiglass for a brighter cockpit. This was also the first time that the characteristic star-shaped five-spoke alloy wheels made an appearance.
Technical specification
Model 365 P SPECIAL
Engine Rear-mounted 60° V12, light alloy cylinder block and head
Timing gear 2 valves per cylinder, 1 overhead camshaft
Bore and stroke 81 x 71 mm
Unitary and total displacement 365.86/4,390.35 cc
Compression ratio 8.8:1
Maximum power 380 bhp at 7,300 rpm
Transmission Multi-plate clutch, 5-speed gearbox + reverse
Chassis Tubular
Front suspension Independent
Rear suspension Independent
Length 4400 mm
Width 1890 mm
Height 1190 mm
Wheelbase, front and rear track 2600/1480/1470 mm
Kerb weight 1,020 kg