I moved from CT to MA in OCt'08. But instead of paying taxes to MA I paid taxes to CT since W2 was not updated.My W2 has only the for CT for whole of the fiscal year 2008 even though I worked in MA from Nov'08.

Now I am wondering if I should file state taxes to both the states or just CT.

You should file in both CT and MA as part-year resident for each. You will pay CT taxes for the period of Jan - Oct, and MA for the period of Nov - Dec. Since only CT taxes were withheld, you will probably find that you get a rebate from CT and owe a fair amount of tx to MA. If you have not already done so, get your employer to start withholding MA tax instead of CT - otherwise you could be penalized by MA for underpayment of witholding for 2009.