Emergency services were called to a house fire.
Police believe the fire started when inflammable material was put through the letter box.
The flames were confined to the front door and it had been put out by the occupants before the fire service arrived.
The incident happened on Thursday at about 2.30am in Juniper Road, Langley Green, Crawley.
An examination of the fire damage revealed that it was deliberately started. The house was occupied at the time but no-one was hurt.
Detective Constable Mark Buckley said: “We remain open-minded about the motive for this isolated incident, and are seeking answers from within the local community.
"If you were in the area at the time or believe you know who is responsible, please get in touch with us, either online or by calling 101, quoting serial 92 of 21/03."
People can also contact the independent charity Crimestoppers on 0800 555 111.
No arrests have been made but enquiries continue.
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