Ducey signed the bill Tuesday funding the special primary and general elections after the Legislature voted to approve the legislation.
Maricopa County estimates the election will cost $3.5 million. The Senate sponsor of the bill has said the county may be able to come back for more cash but there is no guarantee.
The costs are for a Feb. 27 primary and an April 24 general election.
Twelve Republicans and two Democrats are on the primary election ballot. Each party’s top vote-getter moves on to the general election.
Franks resigned Dec. 8 amid sexual harassment allegations.
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