We study the Kennicutt-Schmidt star formation law and efficiency in the gaseous disk of the isolated galaxy CIG 96 (NGC 864), with special emphasis on its unusually large atomic gas (H I) disk (rH (I)/r(25) = 3.5, r(25) = 1.'85). We present deep Galaxy Evolution Explorer near- and far-UV observations, used as a recent star formation tracer, and we compare them with new, high-resolution (16 '' or 1.6 kpc) Very Large Array H I observations. The UV and H I maps show good spatial correlation outside the inner 1', where the H I phase dominates over H-2. Star-forming regions in the extended gaseous disk are mainly located along the enhanced H I emission within two (relatively) symmetric, giant gaseous spiral arm-like features, which emulate an H I pseudo-ring at r similar or equal to 3'. Inside this structure, two smaller gaseous spiral arms extend from the northeast and southwest of the optical disk and connect to the previously mentioned H I pseudo-ring. Interestingly, we find that the (atomic) Kennicutt-Schmidt power-law index systematically decreases with radius, from N similar or equal to 3.0 +/- 0.3 in the inner disk (0.'8-1.'7) to N = 1.6 +/- 0.5 in the outskirts of the gaseous disk (3.'3-4.'2). Although the star formation efficiency (SFE), the star formation rate per unit of gas, decreases with radius where the H I component dominates as is common in galaxies, we find that there is a break of the correlation at r = 1.5r(25). At radii 1.5r(25) < r < 3.5r(25), mostly within the H I pseudo-ring structure, regions exist whose SFE remains nearly constant, SFE similar or equal to 10(-11) yr(-1). We discuss possible mechanisms that might be triggering the star formation in the outskirts of this galaxy, and we suggest that the constant SFE for such large radii (r > 2r(25)) and at such low surface densities might be a common characteristic in extended UV disk galaxies.