It said Zhaxi Sangwu had "managed to run away from the police station on Saturday on the excuse of using the bathroom".
The man apparently swam across a river to escape and was still missing.
Rioting broke out in Tibet's regional capital Lhasa on March 14 last year after days of protests against Chinese rule by Buddhist monks, killing 19 people and sparking waves of protests across Tibetan areas.
Groups of Tibetan exiles say more than 200 people died in a crackdown.
A year later, troops and police across Tibetan areas have apparently helped deter any flare-up of unrest.
However, in recent weeks, a monk set himself on fire at the Kirti monastery in western Sichuan and a bomb was thrown at a government office, which caused no casualties.