I am GC holder ready to apply for citizenship. I have my permanent residence in Pittsburgh, PA, I own a house there, I receive my mail there and I pay taxes there too. My family lives in Pittsburgh. Couple of months ago I got a job in Memphis, TN, and I'm working there now, living in a rented apartment. All my current employment records show my address being in Memphis TN, and I needed to do so because of benefits, such as medical coverage for me and my family. However, my pay check is deposited in my old bank in Pittsburgh. I still have my PA driving license, I did not apply for TN driving license, and I did not register my car in TN-I still have PA license plates on it. I did not notify BCIS of any change of address.
Where should I send my N-400 Application for naturalization? To Vermont Service Center(as a resident of Pittsburgh, PA) or to Texas Service Center (as a resident of Memphis, TN)? What kind of documents do I need to show to BCIS to prove my residency? Do I need to notify BCIS of my change of address?
Best Regards,
JD85767

An AR-11 is not required for temporary addresses. You indicate that your permanent residence is in Pittsburgh. If that is the case then you would file with VSC. Don't forget that one of the requirements for filing an N-400 is that you live in the district in which you are filing for 3 months before you apply. It appears that you will have met this obligation if you file through VSC based on your PA address.

Thanks. What is in fact the definition of "permanent residence" from INS point of vue?
Is it related to the work place address or to the home address? I'm worried thay may consider my permanent address being in Memphis.
Best wishes,
jd

What Should I Include?
For the Form AR-11: Complete the information requested on the form, including present address, last address (most recent only), alien or registration number, country of citizenship, date of birth, and your signature.

You do not need to include temporary addresses as long as you maintain your present address as your permanent residence and continue to receive mail there.

When sending us a change of address, you do not need to include numerous last addresses; only the most recent last address is needed.

Be sure to also indicate in the appropriate block on the AR-11 your current employment and school, where applicable.

http://uscis.gov/graphics/howdoi/address.htm