Relatives say Safarali Sangov, 37, died on March 5 several days after he was beaten and taken from his house by plainclothes officers.
Police say Sangov, who they suspected of drugs possession, tried to commit suicide by jumping out of a first-floor window during his interrogation at a Dushanbe police station.
Interior Ministry spokesman Mahmadullo Asadulloev told RFE/RL on March 5 that a forensic examination supported that police account. He said investigators have opened an inquiry into Sangov's death.
Officials from the Interior Ministry's department for Internal Investigations confirmed today they have also embarked on a separate probe.
Zarif Alizoda, Tajikistan's ombudsman, is also following the case and told RFE/RL today that his team will visit Sangov's relatives on March 8.
Sangov's wife told RFE/RL that on March 1, a group of men in civilian clothes, who were evidently from a police station in Dushanbe's Sino district, entered their house, beat her husband, and took him away.
Sangov's relatives found him later in a coma in the resuscitation department of one of the city's hospitals.
Boboi Sulaymon, an elderly relative of Sangov, told RFE/RL on March 5 that Sangov died earlier that day and had already been buried.
Interior Ministry spokesperson Asadulloev said the police officers suspected Sangov was in possession of drugs. He added that Sangov had been arrested previously for crimes in Russia and Tajikistan.
Sangov's relatives acknowledge he was jailed in Russia in 1998 for five years for drug-related crimes. But they also say that when he returned home he went into business and opened a small supermarket. They say police were trying to extort a share of his profits.
Some 85 Tajik Interior Ministry personnel were fired last year for various crimes, but not one for torture. International and local human rights activists and journalists who suspect torture is widely used in police detention say that torturers are usually charged with abuse of their official position.