If our company is in California and we do a job in another state, do we pay employment taxes to that state or California?

1. If you are present in any state, income earned during that period must be reported to that state.
2. You must report your worldwide income for the year to your resident state.
Read: Your U.S. Tax Return: Working or Living in Two or More states

By employment taxes, I assume that you meed unemployment and/or disability.

The answer is probably NO, but it depends on the duration of the job and the individual state tax laws. A phone call to the state tax authority should get you an answer.