Kenyan police say the 33-year-old runner was discovered with an AK-47 rifle and 23 rounds of ammunition at his house near Iten in Elgeyo-Marakwet county.
Sub-county police commander Tom Makori said a woman had reported Robertson for sexually assaulting her during a house party this week, according to Kenya’s Standard newspaper.
The firearm and ammunition were found while he was being questioned in relation to that.
"The suspect has been living in Kenya for several years," the police commander told the Standard.
"He has bought land and built his residence. Our preliminary investigations indicate that the AK-47 in his possession was unlicensed."
The policeman said that Robertson had declined to open the door when police arrived to arrest him for questioning about the sexual assault allegation.
The Hamilton-born Robertson holds Oceania and New Zealand long-distance records and won bronze in the 5000m at the 2014 Commonwealth Games. He also competed in the marathon at the Tokyo Olympics two years ago.
Robertson was suspended by the Sports Tribunal for eight years after a prohibited substance was found in his system. He also tampered, or tried to tamper, with part of the doping control process, the Sports Tribunal announced.
The Tribunal banned him for four years for the presence and use or attempted use of the prohibited substance Erythropoietin (EPO) and another four for tampering.
Speaking on the podcast Runner’s Only with Dom Harvey, Robertson opened up about why he decided to cheat, claiming it was a "one-off".
"It’s been a pretty depressing and devastating day for me," he said on the podcast.
"There’s many reasons and it’s just not one particular reason. I hate it so much that it’s just a one-off hit and I got caught. It’s been building on me for a few years. Frustration and anger at the sport itself and any elite sports, I just believe it’s not a level playing field like they say.
"I started to ask myself this question: why do people like myself always have to be the ones to lose or suffer. In the end, lose our contracts, lose our income, lose our race winnings, and eventually give up not having the ability to have a family ... that was one reason."
He added that personal and professional troubles – including a "nasty divorce" – also drove him towards doping.
"The other [reason], especially after the Covid era, prize money and races went down. Contracts were almost dropped as well. After the Olympics I was told by one of my companies we thought you would run better, and an immediate exit from the deal.
"Nothing was seeming to go my way. I had a lot of background noise away from the running year as well ... I spent a lot of my life savings just trying to survive. I was providing for myself and my wife at the time ... we already knew we were going to go through a divorce period. It was a nasty divorce proceeding.
"Some things led to another and a lot of stress was placed on me. I made some bad decisions in a really dark time."
The 33-year-old said his attempt to cover up the result during the doping process, which added another four years to his suspension, was his last-ditch attempt to save his career.
"I want to take full blame for that as well. That was my idea. To me four years is the same as eight. It’s the end of my career. There’s no coming back from this and I knew. I was just trying to save my arse."
Known for training in Kenya with his twin brother Jake, he moved up to the marathon distance, finishing 36th at the Tokyo Olympics.