Four men fled a closed ward at the Weissenhof Clinic in Weinsberg (Heilbronn district).
The men, including three convicted criminals, are considered dangerous and may be armed, the police said on Thursday.
A police spokesman said there had been no concrete evidence of weapons so far.
"But of course we can't rule it out." The authorities warned against taking hitchhikers with you.
When looking for the fugitives, the investigators rely on clues from the population.
The police published names and descriptions of the four men between the ages of 24 and 37, and photos of them were published by the State Criminal Police Office.
Witnesses were asked to report suspicious persons.
According to a spokesman, a police helicopter was also used in the search for the four men; further details about the search were initially not wanted for reasons of tactical investigations.
It is unclear how the escape was possible
The police initially left other questions unanswered.
Why the four men had been housed in the closed ward and in the clinic for the penal system remained just as unclear as the question of how they could escape from the complex on Wednesday evening around 10:00 p.m.
The penal system is about the accommodation of mentally ill or addictive offenders.
The aim is to protect the population and provide therapy for patients.
The Klinikum am Weissenhof, Center for Psychiatry Weinsberg, is an academic teaching hospital of the University of Heidelberg.
It is under the supervision of the state of Baden-Württemberg and offers psychiatric, psychotherapeutic and psychosomatic treatment and care for mentally ill people in the Heilbronn region.