"Someone's Watching Me!" is a 1978 film written and directed by John Carpenter and starring Lauren Hutton, David Birney and Adrienne Barbeau.
Leigh Michaels (Hutton) moves from New York to LA to get away from a bad relationship. First thing she does is rent an apartment in a downtown highrise building on the 42nd floor. She also secures a job a local TV station. That's where she meets her new friend Sophie (Barbeau).
Shortly after moving into her apartment, she gains the unwanted attention of a peeping tom who spies on her with a high powered telescope from another high rise. Not only does he visually spy on her, he also plants a listening device in her apartment so he can hear her. He also starts calling her and sending her unsolicited gifts.
She solicits the help of her new love interest, Paul Winkless (Birney) in trying to find out who the stalker is. She also tries going to the police but this being 1978, they had yet to develop anti-stalking laws so basically the police can do nothing until something bad happens to her.
A little slow to get going but nice cat and mouse action in the last third of the movie finally gets makes it interesting.