The devastated family of a murdered Long Island woman believes two mysterious calls from a Boston number — one lasting 17 minutes — to her cellphone around the time she disappeared may be the key to solving who killed her.

But Rebecca Koster's loved ones say Connecticut detectives have been unable to track down who called at about 4 a.m. on Dec. 4.

"We have no idea who this number belongs to," Koster's stepfather, Larry Ross, said yesterday. "This could be the key."

Ross, who said he'd been told the number was a prepaid AT&T cellphone, says his family has repeatedly dialed it.

On several occasions, someone appeared to answer and hang up without speaking, leading the family to wonder whether they had the killer on the other end.

The phone's voice mail feature had not been activated.

Connecticut State Police are investigating the murder of the 24-year-old home-health aide, whose stabbed and burned body was found dumped in a field in North Stonington. All they would say yesterday was, "We do not discuss details of an ongoing investigation."

Ross said cops were looking into the possibility that the killer may have used a ferry to cross Long Island Sound into Connecticut.

The Orient Point-to-New London ferry docks 13 miles from where the body was found just north of I-95, a main route to Boston. The Port Jefferson-to-Bridgeport ferry leaves a short distance from where Koster was last seen at the Butcher Boy Bar and Grill in Holbrook, LI.