I don't remember much. Just that it starts on a large space ship passing near earth. There's a big door to a cell and something happens and the creature escapes and goes to earth. It kills people the cops follow it. One of the alien cops tries to help. Seems like it was a woman but I don't remember. I know at one point it tried to copy her and was draining her memories and the other person commented that if it had finished she would have forgotten how to even breath.
Perhaps Something is Out There, a 1988 NBC miniseries followed by a regular series?
Jack Breslin (Joseph Cortese) is a police officer investigating brutal murders in which organs have been removed from the victims. He learns that the crimes are being committed by a monstrous alien insectoid prisoner known as a xenomorph, possessing shape-shifting and physical possession abilities, who has escaped from an alien prison starship passing by the solar system, and he teams up with a beautiful medical officer from that ship, Ta'Ra (Maryam d'Abo), to track the villain down. Ta'Ra has assorted superhuman abilities, including telepathy and superhuman agility, which come in handy during the mission.