The balloon-borne experiment FIGARO II was launched from the base of Trapani-Milo on July 9, 1990 at 0433 UT and observed the Crab pulsar for about 5 hr. The light curve of the signal from PSR 0531 + 21 folded with the radio period shows clearly the known double-peak structure. The spectrum of the second peak, the dominant structure in the hard X-rays and low-energy gamma rays, is characterized by a feature which, if interpreted as an emission line, gives the intensity of (0.86 {plus minus} 0.33) {times} 10 to the {minus}4th photons/sq cm per sec at the energy of 0.44 {plus minus} 0.01 MeV at a confidence level of 99.6 percent. If this feature is the signature of positron annihilation close to the neutron star surface, redshifted by the intense gravitational field, it is possible to estimate the mass-to-radius ratio of the Crab neutron star and the positron production rate from one of the polar caps. The former is equal to 0.087 solar masses/km and the latter 8.2 {times} 10 to the 39th e(+)/s for a pencil-beam pattern, in reasonable agreement with some heuristic estimates based on the number of energetic particles radiating the optical pulses. 16 refs.