A flammable liquid was poured through the postbox of a home in Lee Mount.
The incident happened at a property on Brighton Street at around 11am on Sunday, June 28.
The liquid was not lit but police are looking to speak to a man who was seen in the area around the time of the incident.
Sgt Dean Maddocks, of Halifax neighbourhood police team, said: “I am keen to trace a male in his early 20s who was in the area at the time of the incident, wearing a grey hooded top and brown khaki trousers.
“The liquid was not ignited or we could be looking at potentially life threatening incident.
“I would appeal to anyone who saw someone acting suspiciously around the time of the incident to come forward.
“This incident took place mid-morning in a residential street and I am certain someone will have seen something. Enquiries are ongoing.”
Anyone with information is asked to contact PC 1223 Hay at Halifax Police Station on 101 quoting crime reference 13150258423.