The aim of this paper is to derive a general procedure for the path integral treatment on compact and noncompact rotation groups as symmetry groups. Analysis of the symmetry of the Lagrangian leads to the expansion of the short time propagator in matrix elements of irreducible representations of the symmetry group. Identification of the coordinates with the group parameters transforms the path integral to integrals over the group manifold. The integration is performed using the orthogonality of the representations. Compact and noncompact rotation groups are considered, where the corresponding path integral is embedded in Euclidean and pseudo-Euclidean spaces, respectively. The unit sphere and unit hyperboloid may either be viewed as the group manifold itself or at least as a group quotient. In the first case Fourier analysis leads to an expansion in group characters. In the second case an expansion in zonal spherical functions is obtained. As examples the groups SO(n), SU(2), SO(n-1,1) and SU(1,1) are explicitly discussed. The path integral on \(SO(n+m)\) and SO(n,m) in bispherical coordinates is also treated.