The issue of dynamical anisotropy in helical three-dimensional magnetohydrodynamic turbulence with a mean magnetic field B₀ is investigated. Using high-resolution direct numerical simulations, we follow the evolution of various isotropic initial states characterized by their different values of the kinetic helicity. The cross helicity and magnetic helicity of the initial conditions are also varied. In agreement with earlier work, we find that such initial states become anisotropic in of order an eddy-turnover time, with correlation lengths parallel to B₀ remaining largely unchanged while finer scales are excited in the perpendicular directions. Moreover, it is found that the development of both the anisotropy and the energy are essentially independent of the initial level of kinetic helicity. The physics associated with this latter feature is discussed.