DOROTHY UHNAK'S new novel, The Investigation, is about a detective trying to discover whether an attractive young woman in New York murdered her small children. Since word of the book got out, people have been asking if it's based on the case of Alice Crimmins (subject of a nonfiction book by Kenneth Gross in 1975). Publishing executives refuse to talk about that aspect, but what they have been willing to do is spend a fortune for the book's subsidiary rights.

Simon & Schuster (part of the Gulf & Western conglomerate) will not publish the book until August, but when the paperback rights went up for sale early this month eight companies spent two grueling days bidding for them. simon & Schuster subsidiary Pocket Books held the floor, as they say, with $250,000 and topping privileges. (PB is the paperback publisher of Uhnak's earlier novel, Law and order.) Eventually the figure to beat was from Pyramid at $1.45 million. Ballantine and Fawcett dropped out. But Pocket Books came back and clinched it for $1.595 million.

Paramount, another chunk of Gulf & Western, has the movie. Which means that the hardcover, softcover and film rights are all now owned by the same conglomerate.