Fire crews were called to an arson attack at Brighouse Library yesterday morning.
They said some kind of accelerant was thrown at the door of the historic building on Halifax Road before it was set alight.
The paint on the door blistered and there was soot damage but the fire did not spread inside the library.
Firefighters, who were alerted at 4.05am, and police are investigating.
They were called to reports of smoke in the doorway.
As spokesman for West Yorkshire Police said: “Investigations are ongoing to see if there were any suspicious circumstances.”
The library is open as usual.
Anyone with information that might help the police and firefighters’ investigation is being asked to call police on 101 or Crimestoppers, where information can be passed on anonymously, on 0800 555111.