A person can get sick and catch what's called the Hantavirus which is spread through Rodents Urine and Feces.
The Hantavirus is usually spread through breathing in dust from the Rodents nest or breathing in the dust from the rodents mice droppings.
If you do need to clean up mice droppings you should wear a mask and gloves and use a vacuum cleaner to clean the mouse droppings up without touching them.