Kirklees District Police do not think the offences which started on Monday are connected.
On Monday, August there was a collision with a barrier at Dewsbury Police Station and a firearms discharge nearby.
Then yesterday there were reports of a firearms discharge in Ravenshouse Road, in Dewsbury, where a man was injured.
Today police attended Spen Valley Road after a suspected arson attack on a parked vehicle.
Four males aged 17, 17, 19 and 29 were arrested in connection with the first incident and remain in police custody at this time.
Dewsbury NPT Inspector Chris Hughes said: “Over the past few days there have been a number of incidents in the Dewsbury area and our communities are understandably concerned.
"I would like to reassure them that we are conducting extensive enquiries into these incidents and want to send a clear message that gun crime will not be tolerated by West Yorkshire Police.
“We believe that all the incidents were targeted attacks, but also unconnected with each other. Kirklees District have ongoing support from specialist armed officers and we have also increased our policing presence in the town as we target those suspected of being involved in criminal activity.
“Anyone who has any information about any of the incidents is urged to contact with police via 101. I would also like to remind the public that they can pass on information anonymously to independent charity Crimestoppers on 0800 555 111.”