CECIL TOWNSHIP, Pa.—An increase in the number of teens and young adults diagnosed with a rare cancer in the southwest corner of Pennsylvania has caused the state to look for a link between fracking and the disease.

The investigation was sparked by a spate of Ewing’s sarcoma cases in and around Washington County, which has more Marcellus Shale gas wells than any other county in the state. In April, the state Department of Health found that the cases didn’t constitute a statistically significant cancer cluster. But affected...