Yes. An SSI beneficiary must report any change in living arrangements within 10 days after the month the change occurs. If you don't, you could end up receiving an incorrect payment and have to pay it back. Failure to report or filing false reports could result in a fine, imprisonment or both. Also, you need to report your new address to Social Security so that you can continue to receive mail from Social Security when necessary. You can report the change by mail or in person at any Social Security office. Social Security's toll-free number is 1-800-772-1213. People who are deaf or hard of hearing may call the Social Security Administration’s toll-free TTY number, 1-800-325-0778, between 7 a.m. and 7 p.m. on Monday through Friday.

You may also wish to read the Social Security Administration’s material on "reporting responsibilities" in the booklet, "Understanding SSI" and in the SSI Spotlight on this subject: http://www.socialsecurity.gov/notices/supplemental-security-income/text-understanding-ssi.htm#report  and http://www.socialsecurity.gov/notices/supplemental-security-income/spotlights/spot-rights-responsibilities.htm.