For highly entangled cis-polyisoprene (PI) star polymers having more than 10 entanglements in each arm, dielectric and viscoelastic properties were examined within a context of the generalized tube model incorporating the dynamic tube dilation (DTD) mechanism. The star PI had the type A dipoles parallel along the arm backbone, and the global motion results in the viscoelastic as well as dielectric relaxation. The DTD relationship between the dielectric and viscoelastic relaxation functions Phi(t) and mu(t), mu(t) congruent to [Phi(t)](2) (derived under an assumption of random displacement of the entanglement segment in the dilated tube edge), was not valid for the star PI. Furthermore, the DTD model (Milner-McLeish model) excellently described the viscoelastic data, but considerable differences were found for the dielectric data, even if an effect of the segment displacement in the tube edge was considered in the model. These results indicated a failure of the DTD molecular picture for a few entanglement segments near the branching point. Thus, these segments near the branching point appeared to fully relax via the constraint release (CR) mechanism before the expected tube dilation was completed. On the basis of this result, the DTD model was modified by explicitly incorporating this CR process (though in a crude way). This modification moderately improved the model prediction, suggesting a possible direction of further refinement of the model.