A nurse who returned home to Maine after treating Ebola patients in West Africa said Wednesday she wouldn’t comply with a state quarantine, keeping a spotlight on a person hailed by some as a defender of individual rights and criticized by others as risking public health.

Kaci Hickox, 33 years old, said she had no symptoms of the disease and stepped out of her house Wednesday night as the state moved to seek a court order enforcing the quarantine. Health officials had wanted her to stay home until Nov. 10, when the 21-day...