In a statement here, Jayalalithaa said an SIT headed by a joint commissioner of police will probe the accident.
She said as the probe needs the expertise of engineers and architects, the SIT is being constituted under the overall supervision of the Chennai city police commissioner.
Jayalalithaa said experts from the Indian Institute of Technology-Madras, Anna University, other universities and the Public Works Department (PWD) will be part of the probe team.
She said six people, including the managing director and director of the project development company, have been arrested.
The SIT probe is in addition to the inquiry commission headed by Justice (retd.) R. Raghupathy that was announced by Jayalalithaa last week.
She said the commission will look into all aspects that led to the building's collapse.
The commission will also determine and fix responsibility for the disaster and recommend measures to be taken so that such accidents do not occur in the future.
However, the statement did not spell out the time frame within which the commission has to submit its report.
The residential project Trust Heights was being developed by Prime Sristi Housing Pvt. Ltd. The project comprised two 11-storey blocks - The Belief and The Faith.
One of the two towers collapsed June 28, killing 61 and injuring 27, while the other tower is also considered as unsafe and is o be pulled down.
Meanwhile, the DMK party has announced it will take out a procession to Raj Bhavan July 12 to press for its demand for a CBI probe into the building collapse, condemning the state government for giving sanction for the construction.