Measure 15-75 would raise $8.3 million annually for Jackson County's 15 library branches by charging property owners 66 cents per $1,000 of assessed valuation.
The three-year levy would add $110.22 in taxes annually on a house with an assessed value of $167,000, the county average.
Ballots went out Friday and must be returned to the Elections Office by 8 p.m. May 15.
Because it is not a general election, 50 percent of registered voters must turn out for the election and a majority of those must vote yes for the levy to pass.
Voters rejected a similar levy in November. In May 2000, they approved a $38.9 million bond measure to build new libraries under the so-called "double majority" rule.
All 15 libraries closed April 6 because Congress failed to renew the Secure Rural Schools and Community Self Determination Act, which provided $23 million to Jackson County annually.
If the levy passes, libraries will operate under the same level of service as before they closed.
Library supporters say the levy will be a bridge to allow enough time to find a permanent solution to keep libraries open.