I agree with everyone else who says I don't think it belongs in your application. I also agree with @BabyScientist that if it comes up naturally during the interview or visitation process I think it is perfectly acceptable to mention it then. I say this because this is exactly what I did during my application process with my partner this year. I never mentioned that I was jointly applying with my partner in any of the application stages but if it came up naturally during an interview or a school visit I would mention it then. I did this because I didn't want to be taken any less seriously and I really was most interested in the science I would potentially be doing with that advisor. I did find though when it came up during an interview or visit it was received well and I don't think I was treated any differently afterwards, at least in my experience thankfully.
I will say though only bring up that this part of your application process if it comes up naturally and you are the one to mention it. I don't think interviewers have the right to ask what your relationship status is because if they maybe didn't choose you because of the relationship component of the application, you would have grounds for a pursuing action of being discriminated against because of your relationship circumstances. So only bring it up if you are the one initiating that conversation and want to be clear that one of the other reasons you are very interested in a program is the proximity it would put you to your partner.
