The incident happened at around 10pm on Wednesday 14 March, when a fire was deliberately started in an extension to the rear of the property.
The Scottish Fire and Rescue Service attended and quickly extinguished the blaze.
Officers are now appealing for witnesses and anyone who can assist with ongoing inquiries if asked to come forward.
Detective Sergeant Lee McCall from Livingston CID said: “Thankfully no one was injured as a result of the fire and it was quickly brought under control by the fire service.
“However, the consequences of this act could have been much worse and we are eager to trace those responsible.
“I would ask anyone who saw any suspicious behaviour in the area, or has information that can assist with our investigations, to contact us as soon as possible.”
Those with information can contact Livingston Police Station via 101, quoting incident number 4117 of 14 March. Alternatively a report can be made anonymously to the charity Crimestoppers on 0800 555 111.