The thought process for this, about this, needs to be out of the typical box. Two of the founding statements is "Peace" & "Unity." Which should be considered first and foremost.
I've seen several of you suggest the less-than-lethal options of OC spray and tasers. Since this would be in a sealed environment, they are not the best of ideas. Add to this that some people just aren't affected by these, especially people with mental derangements and/or chemical addictions. The electricity coming out of a taser shouldn't enough to "fry" or disable advanced electrical systems like we should have in a space station or colony. Sometimes it's not even enough to slow a human being down. The OC spray contaminates anything it comes into contact with, and wouldn't be a good idea in a seal atmospheric system. And it also doesn't effect some people. I don't believe either of these would be good ideas for a security force in space. Some have mention tranquilizers as an option. Not a good idea, as they don't have an instant effect and must be dosed properly for the target's body weight - too much can kill them, too little won't effect them. Some have mention salt rounds, bean-bag rounds and some electro-shock rounds. These are the same as the OC spray and tazers - they just don't effect some people. The armament for the security should be effective, instant and be dependable.
Some have even made comments like "if the police don't want to fight, then they shouldn't have signed up for the job." Which is true. But, officers that get into physical fights get injured. Injured officers require medical attention. Then they'll need either light duty assignments to recover, or medical leave to heal from the injuries. One of the primary goals of a police/security force, besides protecting citizens and arresting bad guys, is to not get injured. That saves wear & tear on their bodies, saves the agency time and money on workman's comp (not to mention the Asgardia government), and keeps the medical staff from having to devote time to repairing the police officers and not taking care of the citizens.
Perhaps a different approach for space security, on stations and on sealed system colonies, is needed. I realize that what I'm about to suggest would an extra expense to any & all future construction endeavors, but all structures built should be compartmentalized (which they would be anyways), or modular construction, so they can be sealed off from the rest of the structure. These modules should also be made of very durable materials (ie - they could take a beating and still function). There would also have to be CCTV cameras in all the modules (except private areas). That way security could monitor all areas, and if for some reason a fight, riot, or some other mass disturbance occurred, that specific module could be sealed off from other areas and the oxygen level dropped low enough to render the people inside unconscious. Although I do think that the security teams on all space platforms need to have access to some kind of lethal weapons, but I believe they should be of a different design that what we have now. As has been mentioned by several of you before - a projectile weapon in a space station could cause more harm than good. Perhaps this is one of the new technologies that we could work on to develop for future use. This is just an idea to hopefully spark some brainstorming for better ideas.
Surface facilities, such as those on Earth, should have an armed force. One of the things that human cultures excel at is trying to kill and destroy anything and anyone that is different from them, for the silliest of reasons. For this reason, Asgardia should have an armed police/military force on the ground. Just because of some of the reasons some of you have suggested - diverge groups that, for what ever reason, don't think we should /be in space/try for racial unity/try for religious harmony/try to be the best that we can - our nation would need to be able to protect itself, and it's citizens and property, from those that might wish us harm.
I guess, to sum up my answer is - Yes, I think the police force should have lethal armament, instantly available to them 24/7, no matter where they are stationed, because humanity always finds a way to become violent for no logical reason.