Injuries on State ferries are considered maritime claims. It does not matter whether the ferry was at the dock or underway. The test to determine whether a maritime claim exists is whether the vessel was in navigation in the navigable waters of the United States.
Typically maritime claims are brought in federal court. But the 11th Amendment prohibits a state from being sued in Federal Court without a waiver.
If you have been injured on a Washington state ferry, you should consider bringing a maritime personal injury claim.