Very light particles with CP-violating couplings to ordinary matter, such as axions or axionlike particles, can mediate long-range forces between polarized and unpolarized fermions. We describe a new experimental search for such forces between unpolarized nucleons in two 250 kg Pb weights and polarized neutrons and electrons in a ^{3}He-K comagnetometer located about 15 cm away. We place improved constraints on the products of scalar and pseudoscalar coupling constants, g_{p}^{n}g_{s}^{N}<4.2×10^{-30} and g_{p}^{e}g_{s}^{N}<1.7×10^{-30} (95% C.L.) for axionlike particle masses less than 10^{-6} eV, which represents an order of magnitude improvement over the best previous neutron laboratory limit.