People who know both men said they are well-known medical professionals in this southwestern Kentucky town.
Rand Paul, who ran for the U.S. presidency previous year, has been attacked at his home in Kentucky.
Boucher was charged with one count of fourth-degree assault.
A spokesperson for Paul told the Courier-Journal in a statement that, "Senator Paul was blindsided and the victim of an assault". Stay with 8News online and on air for the latest updates.
State troopers responded to a call to the senator's residence at 3:21 p.m. Friday.
Boucher is being held at the Warren County Detention Center on $5,000 bond. "Senator Paul is fine".
Hodges said Boucher would have faced more serious charges if had he used a weapon or if Paul had been injured seriously.
"We are working with our state and local partners to determine if there was a violation of federal law", Habich said.
The investigation is ongoing. Both are residents of Bowling Green, Kentucky, where the attack took place.
Rand Paul tweeted about the incident on Sunday morning saying: "Kelley and I appreciate the overwhelming support after Friday's unfortunate event. Thank you for your thoughts and prayers".