Arsonists used petrol to set fire to a flat door while three people were inside.
The attack happened in Livingstone Walk, Grovehill between 4pm and 4.30pm on Monday (February 29).
The victim, a woman who was at home at the time, heard a knock at the door before noticing smoke.
Two men, who were also inside the Hemel Hempstead property, extinguished the flames.
Police believe the incident may be linked with an altercation that happened earlier on the same day between 10am and midday outside the flats, which involved a number of men.
Officers are appealing for information that could help their investigation.
Detective Constable Colin Knowles said: “I would like to speak to anyone who witnessed the disturbance earlier in the day or the arson incident in the afternoon.
“I am also keen to speak to anyone who saw someone walking around the Grovehill area during the relevant times carrying a petrol can.”
Anyone who has any information is asked to contact DC Knowles via Hertfordshire Constabulary’s non-emergency number 101, quoting crime reference D1/16/1592.