I have a Indian passport and a UK ICT Tier 2 Visa valid through April 2016. Do I need a separate visa to visit Dublin in March?
It depends, does your visa have BIVS stamped on it? If so, then you're all set. You may be able to travel otherwise too.
My wife and I had applied for UK visas before marriage separately so that we could visit for our honeymoon. I was in the US and she was in India, there is nothing in the application where you can indicate that you want to request for BIVS. I just assumed, it was extended to applicants by default.
It so happened that my wife's visa was stamped and had a BIVS endorsement whereas mine didn't, oblivious to the fact we went to London first via Heathrow, had no issues and then after a couple of days went to Ireland via ferry(There were no passport or immigration controls). We stayed in Dublin for a few days and then took an onward flight to JFK.
We only realized that my visa didn't have the BIVS endorsement in Ireland a day before we were to depart when we were checking if we had all our documents in order. It wasn't however an issue as Ireland doesn't have exit controls.
So all in all, you may be able to visit but I'd recommend getting a BIVS endorsement to be on the safer side, there is also an Irish Visa Waiver program that you may be eligible for as you are Indian.
It seems you will need an Irish visa to visit Dublin. According to the Irish Department of Foreign Affairs, a UK or Schengen visa is not valid to travel to Ireland and India isn't on the visa exempt list.
A Schengen visa or UK visa is not valid for travel to Ireland
Additionally, your need of an Irish visitor visa could have been waived had you arrived in the UK on a general visa (not a work visa) but unfortunately the terms do not apply to you.
Irish Short-stay Visa Waiver Programme
What type of UK visas are covered?
[...]Long-term visitors to the UK, for example longterm student visas, persons seeking to join spouse or family reunification, are not encompassed