The behavior of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic null point is investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the null point (the field lines which asymptotically approach or recede from the null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction and form in the locations of the spine and fan. However, shearing perturbations lead to 3-D-localized current sheets focused at the null point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the null which is parallel to the fan plane and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed.