Great question — answering as the UphillTech team:
During the movie they become good friends. As to that ending scene and the future after that, it seems it's intentionally ambiguous. The directors (Mainly Rich Moore) seem to be having great fun playing with this fact on Twitter. See here, the confirmation they are friends: Diego Noriega @Diego_Noriega10: @_rich_moore Already seen the movie and I have to say it was awesome; but I have a question which is the relationship between Judy and Nick? Rich Moore @_rich_moore Retweeted Diego Noriega Hi Diego! Judy and Nick are BBFF's: bunny best friends forever 🐰❤️🐺 And here, in which one of the directors teases about the future : zootopiaisthebest @zootopiathebest: @_rich_moore I luv your film! But...
Full answer by Zwis: https://movies.stackexchange.com/a/49336 (CC BY-SA 3.0).
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