Need help: Can I still pursue my master degree?/

I am an H-1 B Visa holder now in California. I wonder if I could pursue a master degree. Actually, I already applied for a part-time degree and got the admission. However, I was told that I couldn't pursue a master degree when holding H-1 B visa. Can I? I remember a long time ago, one lawyer told me that I could go to school and only need to pay the tuition the same as a resident pays. Is that true? Thank you so much for helping out!!!