No, you don’t need to take any permit to visit Spiti Valley if you’re an Indian. But you will need a vehicle permit for Rohtang Pass if you are going to Spiti via Manali side. Also, foreigners need to submit a photocopy of an entry permit called the Inner Line Permit, or ILP which lets them enter into the restricted areas. This can be obtained at the DM offices situated in Shimla, Reckong Peo, Manali, Rampur and Keylong.