Connecting arduino and separate power supply grounds
You should be able to connect your arduino ground to the 24V ground, unless the power supplies are somehow referenced to one another. If one or the other or both of your supplies happens to be a battery, then you don't have a concern. If both supplies are transformer isolated AC supplies, you shouldn't have a problem. Even if both supplies tie their DC return side to the earth-ground lug of the AC mains, you should be ok.

If you bridge the two grounds through a 10K resistor, and a DVM across that resistor shows anything more than a volt or so, your supplies probably aren't isolated enough to just connect the grounds.