The Tennessean reports the board voted Tuesday to approve At-large Councilwoman Erica Gilmore's move to issue the request.
Gilmore is a mayoral candidate in the city's special election next week. The veto request means the council joins Metro school board members and the city's police chief in concerns over the bill.
The bill would require local law enforcement to comply with U.S. Immigration and Customs Enforcement requests to hold immigrants who entered the country illegally. It also would block state or local governments with "sanctuary" policies from receiving a grant from the state Department of Economic and Community Development.
The bill was sent to the governor last month.
Information from: The Tennessean, http://www.tennessean.com
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