The two men, aged 32 and 29 years old, and the 37-year-old woman were forced to evacuate their house after the plastic garden shed was deliberately set on fire in the Boghall area of Bathgate around 11.15pm on Friday night.
The fire spread to their house and the occupants managed to raise the alarm after getting out of the property uninjured.
Detective Constable Craig O’Mara said: “Thankfully none of the people in the house were injured but the fire has caused significant damage to the house as well as the shed in the garden. At this stage the motive has still to be established.
“Limefield Crescent is a residential area and although at this time of night there may not have been people out in the street, it is quite possible people in the houses around the area may have seen something out of the ordinary, someone they didn’t recognise hanging about or indeed who started the fire.
Anyone with information about the wilful fireraising is asked to contact the police on 101.
John graduated from Telford College in 2010 with an HNC in Practical Journalism and since then he worked for the North Edinburgh News, The Southern Reporter, the Irish News Review and The Edinburgh Reporter. In addition he has been published in the Edinburgh Evening News and the Hibernian FC Programme.