The features of the Stark effect of centrosymmetric molecules in a static homogeneous electric field are discussed. Laser Stark spectroscopy has been performed on naphthalene molecules in a collimated, seeded supersonic beam. The Stark splittings and shifts of several rotational lines in the 8(0)1 band of the electronic 1B3u <-- 1A(g) transition could be measured in a static homogeneous electric field ranging up to 300 kV/cm. This is the first experimental determination of electronic excited-state static polarizabilities on a free polyatomic molecule. The polarizability anisotropies of the 1B3u excited state of naphthalene are P'(aa) - P'bb = 10.2 angstrom 3, P'bb - P'cc = 6.6 angstrom 3, and of the 1A(g) ground state, P"aa - P"bb = 6.5 angstrom 3, P"bb - P"cc = 7.6 angstrom 3. In this experiment, only the difference of the average polarizability between these states can be determined, and was found to be DELTA-P = P' - P" = 1.6 angstrom 3.