Q 1. What is my residency status in all these states? CO, CA, and PA?
A 1. From what you described*, you are a full year resident of CO. You will file a resident CO return, reporting all your income. CO will give you a credit for tax paid to any other state. You will file a CA non resident return and pay CA tax on you CA source income. You will not file a PA return, just for being a student there, unless you also earned income there. In which case you will file a PA non resident return. CO will give you a credit for that too.
Q 2. Am I required to file taxes in state of Colorado even though I did not make any income in this state?
A 2. Yes. This is the general rule: The income is work state (WS) source income since it was earned there. Resident States (RS) tax all their resident's income, regardless of where earned. You will file a non-resident tax return for the WS and report the WS income. You will file a full year resident return for the RS, reporting all your income. The RS will give you a credit, or partial credit for any tax paid to the WS.
Q 3. Rolled over 401k from my old job to my Roth IRA and I have earned some dividends from stocks, which states am I claiming these earnings to?
A 3. Report that only on your CO resident return.
*Your time in CA is clearly a temporary absence from your resident state. Being away at school is (almost) always considered as a temporary absence.
