The not guilty plea came six days after Boucher reportedly tackled Paul to the ground as the Senator was mowing his lawn, though the exact details of the incident, and what spurred the bad blood between the two men has not been spelled out in public.
Boucher's lawyer says it has nothing to do with politics.
Paul's office issued this statement a few hours after the first court hearing.
In a series of Twitter posts on Wednesday, Sen. Paul - who has remained at home recovering from his injuries - said he had six broken ribs, and fluid around his lungs from the attack.
"I appreciate all of the support from everyone," Paul tweeted.
Paul also used two tweets to push back against press reports which said the dispute between the two men was somehow related to landscaping issues at their adjoining homes, as Paul posted links to two different stories.
Boucher's attorney said it was a 'regrettable dispute,' labeling it 'trivial' in nature, but offering no details.
It is not clear when Paul might return to Capitol Hill.
The attack on Paul is the most serious personal injury suffered by a member of the U.S. Senate since the late Sen. John Stennis (R-MS) was mugged and shot twice outside of his home in Washington, D.C. in 1973.
Stennis recovered from his wounds, and continued to serve in the Senate until his retirement in January 1989.
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