A suspect has been arrested after armed police supported by a police helicopter patrolled parts of the Abbots Road estate on Sunday December 27.
Measures have been put in place to protect those that were most impacted by the incident.
On December 29, Finkle Street in Selby town centre was closed down for a significant amount of time during a serious incident.
The investigation remains ongoing.
The two incidents were not linked and although serious, they do not present a significant risk to the Selby community as a whole.
No one is currently outstanding as wanted for either incident.
A statement from Inspector Martin Wedgwood from Selby Neighbourhood Policing Team said: "Selby Police have had a really busy Christmas period this year with a number of serious incidents taking place, particularly in the Selby Town area.
"Two incidents of note occurred on Sunday the 27th December and another this morning, both have received a lot of social media attention from residents.
"It is important for the residents of Selby Town to know that these two incidents are not linked and although they are serious in themselves, neither present a significant risk to the community as a whole.
"The first incident saw parts of the Abbots Road estate patrolled by armed officers supported by the police helicopter. The suspect was arrested after an a short search and measures have been put in to place to protect those that have been most effected by the incident.
"The second incident, this morning, occurred in the town centre and saw Finkle Street being closed down for a significant amount of time. Again, although this was a serious incident that required this level of attention it was not an incident that is likely to have an impact on the wider community. The investigation remains ongoing and further details will be released as we are able to do so.
"I can confirm that at this time no persons are currently outstanding as wanted for either incident.
"I would like to thank the public for their patience and support."