Hindu God Shiva is never worshipped with Tulsi leaves. It is also not offered during pujas, rituals and festivals associated Shiva. The reason for this is mentioned in the Shiva Purana.
Legend has it that an Asura named Dambh did not have any children. So he did intense Tapas for several years and pleased Vishnu. When Vishnu appeared before him, he asked for a powerful and invincible son. Vishnu blessed him with a son. Later a son was born to Dambh and he was named Shankhchud. Some scriptures refer to Shankhchud as Jalandhar
Shankhchud wanted to be a conqueror of the three worlds and with this intention he performed tapas and pleased Brahma. As a boon he asked Brahma that no gods should defeat him. Brahma blessed him with Sri Krishna Kavach and advised him to marry Tulsi daughter of Dharmadvaj. Brahma told him that the boon depended on Sri Krishna Kavach and chastity of Tulsi. Tulsi is mentioned as Vrinda in some holy texts.
Once he attained unimaginable powers, Shankhchud attacked the three worlds and conquered it. He started committing numerous atrocities on people, saints and Devas.
People prayed to Shiva and Vishnu to alleviate them from the Adharma of the demon.
Vishnu then took the form of a Sanyasi and asked Shankhchud for the Sri Krishna Kavach. The demon in a moment of weakness parted with the Sri Krishna Kavach.
Next, Vishnu appeared as Shankhchud and breached the modesty of Tulsi.
Then a battle took place between Shankhchud and Shiva and Shiva burned the demon into ashes.
Tulsi, who had to suffer for no fault of her later, attained divine status and was given a boon by Vishnu that she will be dear to him and will become part of him. Tulsi became the divine plant. This is why Tulsi is considered holy.
As Shiva had killed the husband of Tulsi, offering Tulsi leaves makes pujas and rituals meaningless. So the Tulsi leaves are not offered to Shiva.