In most cases, the answer is yes. As of February 2017, here are a list of caveats:
1. HSA contributions are taxed by Alabama, California, and New Jersey.
2. These states don’t have state income taxes so the state tax benefit is not applicable: Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington, and Wyoming.
3. These states tax any HSA earnings (e.g., investment gains, interest earned), but not HSA contributions: New Hampshire and Tennessee.
Please be sure to consult with a tax professional and this is not intended to provide any tax or investment advice.
Source: U.S. Department of the Treasury. Health Savings Accounts (HSAs)
Source: State Actions on Health Savings Accounts and Consumer-Directed Health Plans, 2004-2017. National Conference on State Legislatures