The answer depends on the context in which the word "state" is used. If you mean the state of matter, there is no difference between the metric and the ancient system. In either system a gas is a gas gas gas (as JJF might say)!
If by state, you mean a geopolitical region, the answer will then depend on what characteristic of the state you wish to measure: most economic measures would not be metric. Mean altitude would be measured in metres (above mean sea level), are on square kilometres, and so on.
kilometers
Kilometer or mile
Kilometres
You would typically use the metric unit of centimeters to measure the growth of your hair.
You would use kilograms (kg) to measure someone's mass in metric units.
You would use the metric unit "liters" to measure the capacity of a hot water tank.
You would use the metric unit "kilograms" to measure the weight of a bag of groceries.
You would use liters (L) to measure the volume of a soda container in the metric system.
I would use centimetres.
A thermometer.
You would use the metric unit "kilograms" to measure the weight of a sack of peaches.
You would use the metric unit "kilograms" to measure the mass of a wardrobe.