Final answer:
Vermont is the state that has the Connecticut River on the border between it and New Hampshire, as well as the West River, Otter River, and Winooki River.
Step-by-step explanation:
The state that has the Connecticut River on the border between it and New Hampshire, as well as the West River, Otter River, and Winooki River, is Vermont.
The Connecticut River forms the border between Vermont and New Hampshire, and the West River, Otter River, and Winooki Rivers are tributaries that flow into the Connecticut River in Vermont.