I am not a US citizen and did not reside in US even for a single day in 2011. I earned some dividend on US stocks that I own from an investment I made in 2003 while I was a resident alien. For this dividend, tax has been withheld and it reflects in form 1042-S provided to me. Do I need to file taxes?

Download IRS Pub 901 to determine if you owe taxes on the dividends, and at what percentage.

If the tax percentage matches the percentage withheld, then NO tax return is required. Otherwise, file Form 1040NR to claim a refund.