Your partner ran into the house and told you they just killed someone? Not long ago there was many videos online (mostly teens doing it to their parents) of people contacting a loved and telling them they just committed a murder to how the person would respond to the situation.
In general, neither turn them in nor help them concealing it. However, If I know the victim it may be different. Giving a think about that, I assume s/he wouldn't tell me unless they're really despair and need urgent help/support. So, In that situation, I might do something as they will listen to me.
The last option unless the person they killed was someone I loved. Then I’d either turn them in or convince them to do it themselves. I’d be very worried about my own life. Did they kill someone on purpose or accidentally?
Combination of the first and third. First I would ask them if they were serious or if it was a sick joke. In any case I would have to seriously rethink the relationship. If they really did kill someone I would try to get them to turn themselves in, if they refused I would turn them in. If justice does not apply to everyone (even including people that I care about) then it is not really justice (part of why I hate the USA is because there you only get the "justice" that you can afford to buy).
Probably shouldn't been more specific but I didnt want to use the word murder, but yes its a purposeful killing
I can't imagine what it's like to have a partner, but if I loved someone who informed me they had killed someone, I would want to know the reason why. Murder isn't excusable, but I would let it go if my partner did it for self-defense, and hear them out if it were for revenge. At that point, I probably wouldn't turn them in, but unless I agreed with the reason, I wouldn't conceal the crime, either. If the reason were very scary, such as my partner turned out to be a serial killer, I'd try as safely as I could to get out of the situation and turn them in...
I would talk them in to turning themselves in. I can’t say that I would turn in my partner because I think it would be too hard and even though they did something horrible I feel like I would be betraying them by turning them in. Instead, I would probably use maybe a guilt trip to turn them in. I would tell them think about the victims family, think about being on the run for the rest of your life. I would not help them conceal it though because then you’re just as guilty.
