Police believe the same person was targeted after a window was smashed and a car was set on fire.
Police said on Friday, December 28, at 8pm, the front window of a first floor flat on Deansgate in Morecambe was smashed using a half brick.
The following day at 6pm, a car belonging to a 41-year-old woman which was parked in an alleyway off Deansgate was set alight.
The Vauxhall Astra car was worth £2,000 and has been extensively fire damaged.
Police believe the two offences could be linked and are appealing to anybody that witnessed anything or with any information to contact DC Tris Hardwick on 101.