I am a non resident allien in US for 2011 (Jan - Dec) and as the tax year is different in India (April-March) I will a non resident in India also based on the number of days stayed. Which country will treat me resident for tax purpose will it be US or India?

You need to be specific.

WHERE did you stay in which country (exact dates, please). Also, WHAT is your VISA status?

Stayed in US from sept 15 2011 till date in US and rest of 2011 in India. I had a L1 which was convered in a H1

STILL not clear; "till date in U.S." tells me NOTHING!

However, if you arrived in the U.S. on 15 September 2011 and spent the rest of the year in the U.S. (until 31 December 2011), AND this is the first time in the United States, you are a non-resident alien and will file Form 1040NR-EZ.

You pay taxes ONLY on your U.S.-sourced income for 2011.

There is one clause in the instruction of 1040 NR-EZ "You do not claim any tax credits". Does this mean I cannot use 1040NE-EZ if I have tax refund cliam for 2011? Please advice

Can I be a non resident in two countries, considering the period of stay provisions of both the countries? Or I need to be a resident of at least one country for tax purpose?

If you stayed in the U.S. for LESS than 183 days in 2011, then you ARE a non-resident for the United States.

I cannot comment on how India perceives your residency status.