Greetings!

1) I have stayed in US for about 4weeks. Is it possible to claim Fedaral and State tax with ITIN number?
2) Please let me the procedure for paper filing with ITIN number

Regards
Uma

If you worked in the US, you would have needed a valid SSN.
ANyway, if you didn't have a valid work permit, you can file using your ITIN. YOu would be a non-resident alien if you stayed only those 4 weeks and are not a permanent resident/citizen. You would need to file a 1040NR or 1040NR-EZ. If your income was less than the personal exemption of $3650 you would not be required to file, however, if you had taxes withheld you can file to get a refund.
YOu just put the ITIN in the box for the SSN. You need to print the return and mail it in.