When a covalent compound dissolves in water, it does not dissociate into ions. Because there are no free electrons or ions in the water (electrolytes) dissolved covalent compounds can't conduct electricity.
Do covalent substances ionize?
Most covalent compounds do not produce ions (ionize) in water. An example is sucrose, C12H22O11. Without ions, solutions formed from these compounds do not readily conduct electricity.
How can covalent compounds conduct electricity?
Covalent compounds conduct electricity by a quantum mechanical effect called quantum tunnelling. We say that covalent compounds do not conduct electricity. But all substances conduct electricity to some extent. Conductivity is a measure of the ability of a substance to pass an electrical current.