Perhaps Reid can be recalled within the State of Nevada
Per brief research: The 18 states allowing for recall are as follows: Alaska, Arizona, California, Colorado, Georgia, Idaho, Kansas, Louisiana, Michigan, Minnesota, Montana, Nevada, New Jersey, North Dakota, Oregon, Rhode Island, Washington and Wisconsin.
Does anyone have more detail?
The old states had provisions in their state constitutions where the state legislature could impeach a US senator and remove him. States that came in during the Progressive Era had recall provisions. However, there have never been impeachments nor recalls of US senators because the courts have ruled that Article VI of the US Constitution, aka the Supremacy Clause, does not permit such removal. The US Constitution sets the rules for eligibility and election of senators and congressmen, and the states may not add their own bells and whistles.
People tried to launch a recall against Sen. Menendez in New Jersey, and the state court ordered it shut down, even though the New Jersey Constitution has a recall provision. The court ruled that existing precedent, such as the Frank Church litigation in Idaho in 1967, held that senators could neither be recalled nor impeached by their state legislatures. This is a Supremacy Clause issue.