Can I wire a refrigerator and dishwasher on the same 20 amp circuit?
Branch Circuits Required
210.52(B)(1) Exception No. 2 specifically says that you can put the refrigerator on a dedicated circuit (that can be 15 amperes instead of 20), but does not require it. The rest of 210.52 says that you have to have at least two 20 ampere branch circuits to supply all the required receptacles in the kitchen, and that those circuits can only serve receptacles in that same kitchen (with some minor exceptions).
If you can meet the provisions in 210.52, and still end up under the load calculations in other parts of the code. AND the dishwasher is cord-and-plug connected, then it is possible to have the fridge and dishwasher on the same 20 ampere small appliance branch circuit. Whether or not this is recommended is subjective, and can be debated in another place.
This means that the refrigerator must be rated less than 80% of the branch circuit rating, for it to be connected to a 20 ampere small appliance branch circuit. This would mean the fridge must be rated less than 16 amperes.
It also means that the dishwasher (assuming it's not a portable unit), must be rated less than 10 amperes.
If it's a portable dishwasher, it can be rated up to 16 amperes just like the refrigerator.
So if you have:
Then it is possible (though maybe not advisable) to have a dishwasher, and a refrigerator on the same small appliance branch circuit.
No, you cannot in the U.S. A refrigerator must be on its own dedicated branch circuit because you don't want another appliance/consumer to trip the breaker and cause your food to go bad. Look up NEC 210.11