But down in Jammu, the state's mainly Hindu winter capital in the plains to the south, 95 percent think Kashmir should be part of India.
Delhi's Centre for the Study of Developing Societies interviewed 226 people in Srinagar and 255 in Jammu for the poll, published in Monday's Indian Express.
Another 47 percent of Pakistanis said they supported independence for Kashmir.
The fate of Kashmir -- known for both its natural beauty and for its bloody recent past -- has been uncertain ever since its Hindu ruler hesitated in choosing whether to join the region to India or the newly formed Pakistan in 1947.
The overwhelming majority of Srinagar's residents think the security forces have too much power. The army is often accused of killing innocent people and other rights abuses, operating under a special law that largely protects soldiers from prosecution.
Around 84 percent of people in Srinagar want to see the return of Kashmiri Pandits, a Hindu community, large numbers of whom fled the region after being targeted by Islamist militants. Many live in refugee camps elsewhere in India.