I recently detected that for the year 2008 I have filed tax returns for NY state and city. (The return was filed by the accountant.) In fact, I was full year resident of Connecticut in 2008. I asked about the mistake to the accountant. He said that there is New York city address in my W2 and that's why he filed the returns for New York. Can I file tax return for 2008 for Connecticut and claim refund from NY?

Yes you can file an amended return with NY State and a new return with CT. I suggest ataching an explanation of why it is that you were not a NYC resident at any time in 2008. Be aware that since you are 2 years late in filing with CT for 2008 if you owe CT any taxes for that year you will be subject to interest charges and possibly penalty for late filing.