Neutron-scattering and magnetic susceptibility studies of single-crystal LiCoPO4 are reported. The neutron-diffraction results indicate that in the antiferromagnetic phase the moments are not strictly aligned along the b axis, as previously reported [R. P. Santoro et al., (1996)], but are uniformly rotated from this axis by a small angle (≈4.6°). This rotation breaks the mirror symmetry along the orthorhombic b axis. Symmetry considerations based on this rotation, on the magnetoelectric effect, and on a recently observed weak spontaneous magnetization along the spin direction, implying a so-far-unknown ferrimagnetic-like kind of weak ferromagnetism, allow one to postulate the monoclinic magnetic point group 2'. The diffraction data are analyzed in terms of weakly coupled 2D Ising antiferromagnets. The large anisotropy in the susceptibility is explained in terms of the single-ion anisotropy and anisotropic exchange interactions. We argue that the alignment of the magnetic moments in the antiferromagnetic phase is detd. by the single-ion anisotropy even though the exchange along this direction is the weakest.