I have been offered a full time job with a company in California, and I will be working remote from my home in Indiana. Do I have to pay state income tax in both states?

[KrisD15]

No, only Indiana. 

California does not enforce a "Convenance of the Employer" rule, so they do not tax remote workers working outside of California. 

[Hal_Al]

Q. I have been offered a full time job with a company in California, and I will be working remote from my home in Indiana. Do I have to pay state income tax in both states?

A. Not if you will be a regular W-2 employee.  If you occasionally go to California, on business, your salary for those days are technically considered California source income. 

On the other hand, if you will be treated as a contractor, or "contract employee", and the income reported on a form 1099-NEC, that income will be taxable by both IN (your resident state) and CA (income source state). You are considered to be self employed.  IN will give you a credit, or partial credit, for any tax paid to CA. 

[TomD8]

One other issue:  you should ask your employer to withhold INDIANA income tax from your pay.  If they cannot or will not do that, then you must make quarterly estimated tax payments to Indiana.  Your resident state of Indiana can tax ALL your income, regardless of where you earn it.

https://www.in.gov/dor/individual-income-taxes/payments-and-billing/estimated-tax/