Narrated ‘Abdullah bin Masud:
The Prophet recited Surat-an-Najm (53) and prostrated while reciting it and all the people prostrated and a man amongst the people took a handful of stones or earth and raised it to his face and said, “This is sufficient for me.” Later on I saw him killed as a non-believer.
Hadith covered before, here.
Narrated Ibn Abbas:
The Prophet (SAW) prostrated while reciting An-Najm and with him prostrated the Muslims, the pagans, the jinns, and all human beings.
The ayah of Surah an-Najm where Sajdah of Tilawat was performed:
فَاسْجُدُوا لِلَّهِ وَاعْبُدُوا ۩
“So fall you down in prostration to Allah and worship Him (Alone).” [An-Najm: 62]
Narrated ‘Ata’ bin Yasar:
I asked Zaid bin Thabit about prostration on which he said that he had recited An-Najm before the Prophet, yet he (the Prophet) had not performed a prostration.
Narrated Zaid bin Thabit:
I recited An-Najm before the Prophet, yet he did not perform a prostration.
Note that in the above two Ahadith, Zayd ibn Thabit is reciting and Prophet (SAW) is listening. Hence, Prophet (SAW) did not prostrate (perform Sajdah of Tilawat). But in the Ahadith above these two, Prophet (SAW) was reciting it himself, and he did perform the sajdah.
We mentioned before that performing Sajdah of Tilawat is not mandatory.
Sujood al-tilaawah, whether during prayer or outside of it, is Sunnah, not obligatory, because evidence to that effect was narrated from the Prophet (peace and blessings of Allaah be upon him), in the hadeeth of Zayd ibn Thaabit and in the hadeeth of ‘Umar (may Allaah be pleased with him).