Is this in response to his investigation(may have something good) into Obama’s Birth Certificate
No.
Justice has been investigating Arpaio for years. This administration has had a hard-on for Arpaio since they were elected.
“In June 2008, the Justice Department began its investigation of MCSO.”
http://www.justice.gov/crt/opa/pr/speeches/2011/crt-speech-111215.html
Not only has the investigation been going on for years, long prior to Arpaio expressing interest in Obama’s birth certificate, but it began when President Bush was still in office.