If I am an employee that does 2-weeks of install work in a different state than I live in, and a different state than my employer, do I still pay different state tax?

I install assets for a company who take my taxes out of my pay. I am sent to different states for about 2 weeks at a time to do installs. Do I need to file state taxes for those two weeks of work or is it all included when a company withholds taxes for me?
I do not live in a state where there is income tax, and I also do not live in the same state as the employer.