HANGZHOU, China—Swiping her son’s half-fare student card through the turnstile here one Monday afternoon, Chen Li earned herself a $6 fine and a reprimand from a subway-station inspector for not paying the adult fare.

A notice on a post nearby suggested more-dire consequences. It warned that infractors could be docked points in the city’s “personal credit information system.” A decline in Ms. Chen’s credit score, according to official pronouncements, could affect her daily life, including securing loans, jobs and her son’s...