Question

Why urea is not an electrolyte in molten state

Answer 1

because ions are not free to move therefore does not conduct electricity by the flow of electrons

Answer 2

As Cryolite, Sylvine and Rock salt have ions in free state (free ions), they conduct electricity in molten state. But in urea $$(NH_2CONH_2)$$ there is no free ions to conduct electricity. So, urea is not an electrolyte in molten state.