A resolution moved by the AIADMK-controlled house said Tamils living in Sri Lanka as well as Tamils of Sri Lankan origin in other countries should take part in the referendum.
The resolution also urged India to stop describing Sri Lanka as a friendly nation and sought an international probe on war crimes during the war against the Tamil Tigers that left thousands dead.
It said those responsible for the alleged war crimes should be tried by an international court.
The Indian government was also asked to impose economic sanctions on the island nation until the "oppression" on Tamils there ended.
Speaking in the house, the chief minister referred to the widespread protests by students in the state demanding action against Sri Lanka over the deaths of Tamil civilians in the war against the LTTE.
She also spoke about the UN Human Rights Council resolution that pulled up Colombo over accusations that many innocent Tamils died in the military blitzkrieg against the Liberation Tigers of Tamil Eelam.
Sri Lanka crushed the LTTE and wiped out its leadership in May 2009, ending one of the world's longest running conflicts.
"India should stop calling Sri Lanka a friendly nation," Jayalalithaa said.
"There should be an international probe on the war crimes during the war (against the Tamil Tigers) and people responsible for that should be tried before an international court," she said.
She described as a victory for her government the Indian Premier League's (IPL) decision not to hold any cricket match in Tamil Nadu if Sri Lankan players were involved.
On Tuesday, she told Prime Minister Manmohan Singh that her government would allow IPL matches in the state only if no Sri Lankan player, umpire, official or support staff took part in the matches.
She accused DMK president M. Karunanidhi of being insincere vis-a-vis the Sri Lankan Tamil issue.
She charged the Congress-led Indian government, of which the DMK was a major partner, with helping Sri Lanka to kill Tamils.
She said Karunanidhi revived the Tamil Eelam Supporters Organisation (TESO) only after his DMK lost power in the state in 2011.
The chief minister said New Delhi had not taken any action on the resolution passed by the Tamil Nadu assembly in 2011 urging India to impose economic sanctions on Sri Lanka and approach the UN to declare those responsible for the "genocide" in the island as war criminals.
Jayalalithaa said it was regrettable that the Indian government was indifferent to the Tamil issue and not respecting Tamil sentiments.
She said she had introduced the new resolution in the house to show "the entire Tamil community's feelings".
Sri Lanka and Tamil Nadu are separated by a narrow strip of sea.
Earlier, Sri Lankan President Mahinda Rajapapaksa Wednesday warned of local and internationally attempts to scuttle peace in the island nation.
Addressing a Sri Lanka Freedom Party ceremony in Colombo, Rajapaksa said it was the right of all Sri Lankans to ensure that peace was protected in the country without falling prey to rumours, reports Xinhua.
Rajapaksa's comments come within a week after a US-sponsored resolution was passed against Sri Lanka at the UN Humans Rights Council in Geneva.
Days later, the US warned that international action may be initiated on Sri Lanka if the island failed to implement the latest resolution adopted at the UN Human Rights Council.
Since defeating the Tamil Tigers, Rajapaksa's government has been under pressure, especially from Western countries, seeking an independent probe into war crimes allegations.