Can I use a Dish TV set top with a Tata Sky antenna?

Theoritally, Yes.

Considering the following points, practically it doesn’t make sense-

1. Dish TV (or any other’s brand) Set Top Box are not sold separately. They come along with Dish, LNB and other accessories, as a connection.
2. Even if you manage to arrange only Set Top Box of Dish TV, then you will have to get the Tata Sky antenna alignment done. This won’t be done by Dish TV service team and you will have to get it done from a local technician.
3. You will not be eligible for any services from Dish TV, not even 1 year warranty.
4. Dish TV receives signals from 3 satellites and hence, uses a special LNB called Monobloc (provided only with HD Premium connections of Dish TV). Tata Sky’s LNB will get you channels only from one (or two) satellite and hence, you won’t be able to enjoy most HD channels.
5. When you get a new Dish TV HD Premium connection at Rs. 1400 only inclusive of all set up and installation cost, then why opt for any other option. Also you get package worth Rs. 750 free for first month. More details at dthconnect.com