The drug addicts fled from the centre on April 6 while taking part in physical exercise, a Zhenxiong County government statement said today.
Police have captured 12 of the runaways and returned them to the centre. They are still searching for the remaining 27 fugitives, the statement said.
Those who were responsible for the escape have been suspended from their posts while an investigation takes place, state-run Xinhua news agency reported.
Yunnan, which has a 4,060-km-long border with Myanmar, Laos and Vietnam, is affected because of its proximity to the notorious "Golden Triangle", one of Asia's two main opium-producing areas.