Lauren Harkin, 23, and her son, Tyler, were rescued from their home at Galliagh Park at 9.50 pm on Sunday night, November 25. by fire men.
A sofa was found set alight against the front door.
Two bins were also set on fire below Tyler’s bedroom window.
Investigating officer Detective Sergeant Jack said: “At around 9:55 pm, it was reported that a sofa was found against the front door of a house and two wheelie bins at the back of the property.
“Both the sofa and wheelie bins were set alight.
“A 23 year old woman and her child were inside the house during the incident.
“Both were badly shaken, as Northern Ireland Fire & Rescue Service attended the scene and extinguished the fire.
“This was a reckless act that could have resulted in fatalities. Whoever was involved wanted to cause death and destruction and their actions should be condemned by the local community.
“Thankfully no one lost their lives but we need anyone with any information to contact police to bring those responsible to justice.
“Enquiries are continuing and we would appeal to anyone who saw anything suspicious to contact detectives on 101, quoting reference number 1306 25/11/18.
“Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.”
Miss Harkin told BBC News NI that when she went to check on her son in bed, she saw flames at the front door.
“I called the fire brigade and they told us to get into the kitchen. There was no way out at all,” she said.
“We had to get lifted out the kitchen window. I was petrified for me and my son, and in shock.”
Miss Harkin said she wants to leave her Galliagh home where she grew up.
“We had to be carried out of our own home by a fireman. I want to thank him so much.
“My son is six next week. It puts things into perspective. We might not be here today.”
Northern Ireland Fire and Rescue Service Group commander Andy Burns said he understood the fire was deliberate.
“The occupants were very distressed,” said Mr Burns.
“There was only one door in and out of the property because this was a ground-floor flat.
“The fire was actually blocking their escape route. The advice they were given was to find a room of safety and make themselves known at the window of the property.
“There was a lot of smoke and this fire could have potentially been a lot worse.”
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