Boucher was charged with assault causing a minor injury.
An Internet search identifies a Rene Albert Boucher, the same name as the man jailed for the Paul assault, as an anesthesiologist in Bowling Green. Due to Boucher's attack, the Republican senator has suffered "minor injury".
Paul, an ophthalmologist, dropped out of the race for president in February 2016 and successfully ran for re-election as a senator.
"The assailant was arrested and it is now a matter for the police", Cooper's statement continued.
Someone named Rene Boucher lives in a gated neighborhood just west of Paul's home, the Bowling Green Daily News reported.
In a statement, Paul spokeswoman Kelsey Cooper said the Republican senator is "fine".
WAVE 3 also reported Boucher was previously registered as a Democrat in Rhode Island.
An investigation is ongoing, police said.
Kentucky State Police are investigating an alleged assault on Sen.