The inner nuclear membrane is functionalized by diverse transmembrane proteins that associate with nuclear lamins and/or chromatin. When cells enter mitosis, membrane-chromatin contacts must be broken to allow for proper chromosome segregation; yet how this occurs remains ill-understood. Unexpectedly, we observed that an imbalance in the levels of the lamina-associated polypeptide 1 (LAP1), an activator of ER-resident Torsin AAA+-ATPases, causes a failure in membrane removal from mitotic chromatin, accompanied by chromosome segregation errors and changes in post-mitotic nuclear morphology. These defects are dependent on a hitherto unknown chromatin-binding region of LAP1 that we have delineated. LAP1-induced NE abnormalities are efficiently suppressed by expression of wild-type but not ATPase-deficient Torsins. Furthermore, a dominant-negative Torsin induces chromosome segregation defects in a LAP1-dependent manner. These results indicate that association of LAP1 with chromatin in the nucleus can be modulated by Torsins in the perinuclear space, shedding new light on the LAP1-Torsin interplay.