As @Jonny has said, the two grounds should theoretically be the same, however there are situations where that not be the case and you could end up with a ground loop.
I would think that connecting signal ground of both devices would be the way to go but I might be wrong. You’re safe to connect to the earth ground screw but if you start noticing noise/humming within your signal path when using the two instruments together you might need to switch it up.