We report on new measurements of inclusive J/psi polarization at midrapidity in p + p collisions at root s = 200 GeV by the STAR experiment at the Relativistic Heavy Ion Collider. The polarization parameters, lambda(theta), lambda(phi), and lambda(theta phi), are measured as a function of transverse momentum (p(T)) in both the helicity and Collins-Soper (CS) reference frames within p(T) < 10 GeV/c. Except for lambda(0) in the CS frame at the highest measured p(T), all three polarization parameters are consistent with 0 in both reference frames without any strong p(T) dependence. Several model calculations are compared with data, and the one using the Color Glass Condensate effective field theory coupled with nonrelativistic QCD gives the best overall description of the experimental results, even though other models cannot be ruled out due to experimental uncertainties.