New Jersey has procedures for recall of elected officials. Those procedures do not exclude members of Congress. On May 25, the New Jersey Supreme Court heard arguments on whether the U.S. Constitution blocks New Jersey from permitting recall of members of Congress. See this story. The case is Committee to Recall Robert Menendez v Wells, A86-09.
The lower court had ducked the issue. It failed to decide that big issue, but said at least the state should let the circulators have blank petition forms. The procedure is so difficult, requiring approximately 1,300,000 valid signatures for U.S. Senate or any statewide race, that it is fundamentally unfair for the judicial system to not say whether such a petition would be honored if it were completed.
No other court has ever ruled on this interesting question, except for a lower state court in Idaho in 1967 that said the U.S. Constitution does not permit the states to have procedures for recall of members of Congress.