Deregistration of branch office with government authorities

Different govt department follow different practice for such matters.  As regards sales tax you must have taken single TIN for all units/offices in Maharashtra and Pune office must have been shown as additional place of business.  You can simply inform the dept by way of letter that Pune office has been closed.  Your same TIN will continue and in annual return you can disclose this fact.

You must have already passed resolution u/s 293(1)(a) or Board resolution noting closure of the office, which can be submitted to all departments.  I don't think separate Board resolution is required for deregistration as such.