"When police are expected to protect the lives of citizens in their homes, work places and in public, it would be a travesty of justice if a citizen dies within the precincts of a police station," she said in her address at the police officers conference here.
She also urged police to strongly contest bail applications.
Jayalalithaa said instances are reported of suspects dying suddenly after developing illness while in a police station or committing suicide while in custoday.
"When you arrest nine lakh people, an odd death in custody here and there may appear to be statistically negligible. But a dead man is not a mere statistic for his loved ones," said the chief minister, who holds the home portfolio.
She also urged police to strongly contest bail applications and ensure expeditious trial in cases.