That's tricky.
1. You are required to pay CA state tax on all your worldwide income starting from the day you moved to CA. If you have no income after that date, you would not be required to file. However, if you don't file, CA may send a letter demanding you pay tax, and at that point you will have to produce a tax return and proof of your move-in date, to show that you don't owe anything. (CA is very aggressive about collecting tax.)
2. If your income is less than $39,000, you qualify for the IRS Freefile version of Turbotax, which is completely free and won't change you for the state. It's a separate web site, and you may have to make a new account and start over from scratch. (This is how it was in the past, it may have changed.)
https://freefile.intuit.com