WASHINGTON — The violent altercation last week that left Senator Rand Paul nursing bruised lungs and broken ribs began over a landscaping dispute between the senator and his longtime next-door neighbor, according to neighbors and three Kentucky Republicans familiar with what transpired.

The precise provenance of the dispute was still a matter of disagreement on Monday. But the back story of the fracas began to come into focus and with it, the realization that Mr. Paul’s injuries could keep him from Washington, where Republicans in the Senate hold only a slim majority, for some time.

Mr. Paul had just stepped off a riding lawn mower on Friday when Rene Boucher, a retired anesthesiologist who lived next door, charged and tackled him. Because Mr. Paul was wearing sound-muting earmuffs, he did not realize Mr. Boucher was coming, according to one of the Kentucky Republicans and a friend familiar with the altercation.

“Rand never saw him coming or heard him coming,” said the friend, Robert Porter, who visited Mr. Paul on Saturday.