The violence has escalated in recent days and erupted in large-scale rioting on Saturday in the hill resort at the peak of the tourist season.
Almost 50 people, mostly police, were injured in riots and arson attacks which have been taking place for more than a week, forcing many visitors to leave.
The unrest intensified on Saturday and a man died as cars were torched and police were attacked by mobs with knives.
Officers responded with teargas and baton charges in an attempt to control the situation.
The director general of West Bengal state police, Anuj Sharma, said: “A man was killed and at least 35 policemen were injured yesterday. Some of them were stabbed in the back.”
He said one officer who intervened in an arson attack was “seriously wounded after protesters slashed his throat”.
Mr Sharma said the dead man appeared to have been shot but the circumstances were still unclear.
Police have denied using live ammunition.
The escalation of the violence was triggered when police raided the homes and offices of members of the Gorkha Janmukti Morcha (GJM), a separatist movement that has long called for a new state of “Gorkhaland” to be carved out of West Bengal.
The group has accused police of shooting dead three of its members during the clashes but police have denied this.
GJM’s general secretary Roshan Giri said: “Three of our comrades were killed and five were critically injured in police firing yesterday.”
He said hundreds took to the streets of Darjeeling on Sunday for a silent protest against “police atrocities”, waving India’s tricolour flag and posters calling for peace.
The hills are famous for the Darjeeling tea and the area is also famed for its “toy train” – a 48-mile uphill ride from New Jalpaiguri.
But the violence has dealt a major blow to the crucial tourism industry, leaving the normally busy destination deserted as shops, schools and banks closed.
As well as the campaign for a new state, tensions have risen recently over a decision to introduce the Bengali language in schools which has infuriated the Nepali-speaking Gorkhas.