By TALBOT LAKE HAVE a vague notion that we wrote a story about Mary Shanley some years ago when she did something notable, but you can’t keep a good cop down ,and here we are again writing about her. Yes, we said cop, for Mary Shanley is the star policewoman on the New York City force. Just recently, they made her a first-grade detective, with a salary of $4,000 a year—the first woman in the history of the city’s police department to achieve that rank. She is death on shoplifters. Her stunt is to look through the papers to watch for the bargains. So do the shoplifters, for they work best in crowds. That is where Mary goes to nab them. Detective Shanley began as a clerk in a lawyer's office, but de cided to try for a city job because of the security it offered and the pension rights. She was the sole support of an ailing mother and a brother suffering from cardiac trouble. Both died a short time ago. She is 37, was born in the area known as Hell’s Kitchen and left parochial high school the first year. Her ambition is to “work hard and hang onto her money.” She has made more than fifty arrests. “I had Anna Cohen, the Boston gal,” she said, listing some of the more famous bag openers she has caught. “Then there was Eleanor McCarthy. She’s interna tional. And Greenhorn Clara. They're all good bag openers. We say they're good when they can go a couple of years without get ting caught. “I just get a feeling I'm lucky, and then I'll go out. One night like that I started walking down Forty-fifth Street and there were two fellows mugging a man in a doorway. Mugging? Oh, I guess that’s just our expression. It means that one fellow had his arm around the man’s throat while the other went through his pockets. I arrested the two of them and took them in. Oh, with my revolver, of course.”