Rags soaked in an accelerant were pushed through the letter boxes of two flats in the Larne Road area of Ballymena.
The arson happened at an apartment block yesterday (Sunday, February 28) just after 11pm.
Damage was caused to the exterior doors of the flats.
However no injuries were reported as a result of the incident.
Anyone with any information should contact police on 101 quoting reference 2008 of 28/02/21.
A report can also be made online using the non-emergency reporting form via http://www.psni.police.uk/
You can also contact Crimestoppers anonymously on 0800 555 111 or online at http://crimestoppers-uk.org/.