Kelsey Cooper, a spokesman for Paul, said in a statement that "Senator Paul was blindsided and the victim of an assault". Police said Boucher "intentionally assaulted" Paul, causing him "minor injury". Stay with 8News online and on air for the latest updates.
Politico reported, citing the arrest warrant, that Paul was tackled from behind, and that "Boucher's altercation with Paul left the senator having difficulty breathing as a result of a "possible rib injury" in addition to bleeding from cuts around his mouth".
Police were not immediately clear on why Boucher allegedly assaulted Paul.
WAVE 3 also reported Boucher was previously registered as a Democrat in Rhode Island.
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Paul, an ophthalmologist, dropped out of the race for president in February 2016 and successfully ran for re-election as a senator. He was licensed in 1998.
In recent months Mr Paul, who is on the libertarian wing of the Republican party, has emerged as one of the fiercest critics of the administration's attempts to repeal Obamacare.
It is not known why Boucher was in his home at the time.
He was held at Warren County Detention Center on a $5,000 cash bond, the state police said.
KSP says the investigation is ongoing.