Field-emission patterns from a clean tungsten tip apex induced by femtosecond laser pulses have been investigated. Strongly asymmetric field-emission intensity distributions are observed depending on three parameters: (i) the polarization of the light, (ii) the azimuthal, and (iii) the polar orientation of the tip apex relative to the laser incidence direction. In effect, we have realized an ultrafast pulsed field-emission source with site selectivity of a few tens of nanometers. Simulations of local fields on the tip apex and of electron emission patterns based on photoexcited nonequilibrium electron distributions explain our observations quantitatively. Electron emission processes are found to depend on laser power and tip voltage. At relatively low laser power and high tip voltage, field-emission after two-photon photoexcitation is the dominant process. At relatively low laser power and low tip voltage, photoemission processes are dominant. As the laser power increases, photoemission from the tip shank becomes noticeable.