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Changu lake permit is obtained in tsomgo lake police check post. You could apply online or through a tour operator. Nathula pass permit can be obtained in Nathula check post. From what I gathered through known travellers is this lake is not closed on public holidays.
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Tsomgo (Changu) Lake and Baba Mandir permits are issued at the Police Check Post. Foreigners can also get it at Sikkim Tourism & Civil Aviation Department. Easiest is to apply through a travel agent or tour operator one day in advance
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