Is there poison oak near San Jose?

Yes, there is poison oak near San Jose. It grows throughout the Santa Cruz Mountains, and some campsites at Henry Cowell Redwoods State Park have a fair amount of it.

Its leaves grow in threes, and in autumn they turn red and drop. Every part of the plant has an oil that gives most people a rash.

In Joseph D. Grant County Park, east of the city, visitors report it most from April through June and October. This is based on 96 iNaturalist observations.