What River Begins Near Rome and Flows Into the Hudson? None—Different Continents

No such river exists. The premise mixes two unrelated rivers on different continents.

The Rivers in Question

• Tiber River (Italy): Rises in Apennines near Rome, flows through Rome, empties into Tyrrhenian Sea at Ostia. Length: 406 km.
• Hudson River (USA): Rises at Lake Tear of the Clouds (Adirondacks, NY), flows south through eastern New York, empties into Upper New York Bay. Length: 507 km.

Why They're Unrelated

• Different continents: Europe vs. North America.
• Different drainage basins: Mediterranean vs. Atlantic (via NY Harbor).
• No hydrologic connection: Atlantic Ocean separates them by ~6,500 km.

Possible Confusion Sources

• Rome, New York – a city in Oneida County, NY. Its river is the Mohawk River (Hudson tributary). But the question says "near Rome" (implies Italy).
• Hudson Valley has Dutch/English colonial history, not Roman.
• Trick question / geography quiz trap.

If you meant Rome, New York: the Mohawk River flows through it and joins the Hudson at Cohoes. If you meant Rome, Italy: the Tiber flows to the Mediterranean. They never meet.