PALM BEACH, Fla.  In the summer and autumn of last year, when most of the mansions here stood empty behind their towering hedges, the police stealthily watched one at the end of a waterside lane. They monitored the comings and goings of its owner’s private jet, subpoenaed his phone records and riffled through his trash.

The owner was Jeffrey Epstein, 53, an intensely private New York money manager with several billionaire clients. Months earlier, the stepmother of a 14-year-old girl told the Palm Beach police that a wealthy older man, whom the girl later identified as Mr. Epstein, might have had inappropriate sexual contact with her.

In sworn statements to the police, the 14-year-old and other teenage girls said a friend had arranged for them to visit Mr. Epstein’s home and give him massages, usually in their underwear, in exchange for cash.

Most of the girls, according to the police, said Mr. Epstein had masturbated during the massages, and a few said he had penetrated them with his fingers or penis. They identified him in photos and accurately described the inside of his home. Some recalled that his employees had fed them snacks or rented them cars.