Over the past week, three apparently unrelated people have been shot dead in the state by an unknown assailant, or assailants, firing a small calibre rifle.
Authorities said each of the victims was shot from a distance at convenience stores.
The first victim, a 44-year-old man, was shot on 10 August while he talked on a public phone in Charleston, the state capital.
Four days later a 31-year-old woman was fatally shot while pumping gas at a convenience store just outside Charleston. Just 90 minutes later a 26-year-old man was killed with a shot to the neck at a store in a nearby town.
Kanawha County sheriff Dave Tucker said on Monday that police believed a "heavy white man" may be a suspect in the case, but declined to "put a name" on the crimes as being sniper-perpetrated serial killings.
"The only thing I can say, it's a small calibre ... there are similarities but I don't say it's the same," Tucker said at a Charleston press conference.
Tucker said that authorities have "a hundred leads ... some very solid" and that among them, police were looking for a recent model dark-coloured pick-up truck, possibly blue or brown.
Washington sniper suspect John Allen Muhammad
"We are actively pursuing possible suspects," he said.
Earlier on Monday, Jerry Pauley, chief of Charleston's police department, told NBC television: "So far we've got some evidence that shows that it could have been the same person or the same type of weapon used."
Pauley said police suspect the shootings may have been random.
"We haven't determined any connection between the three victims," he said.
FBI agents - some of whom worked on the Washington sniper shooting case - have been called in to assist in the West Virginia investigation.
In the Washington sniper case, which is scheduled to go to trial in Virginia in October, John Lee Malvo, 18, and John Allen Muhammad, 42, face the death penalty for allegedly killing 10 people and wounding three others in the suburbs of the US capital last autumn.