What role does Intuition (as in a “hunch”) play in Kant’s moral philosophy? Imag

What role does Intuition (as in a “hunch”) play in Kant’s moral philosophy?
Imagine that you have hidden some Jewish people in your basement in Nazi Germany. Imagine then that an SS officer knocks at your door and asks if you are hiding Jews?
What might Kant’s theory tell us to do? Our duty is to refrain from lying so does this mean we are morally required to tell the SS officer our secret? Suppose that we have promised to keep these refugees safe.
How might Kant respond to this criticism of conflicting duties?