A Silicon Valley transit agency can soon start distributing $340 million in tax revenue stuck in an escrow account during a legal battle thanks to the California Supreme Court.

Justices Jan. 23 denied review of a taxpayer challenge to the 2016 voter-approved half-cent sales tax, meaning the Santa Clara Valley Transportation Authority can soon start distributing the funds the tax raised for transit and transportation projects.

“VTA is now working to get this matter back to the trial court for a final order so that the funds may be released,” the agency said in a news release.

The tax...