The Messenger of Allah ﷺ would not perform ablution after the ritual bath.
أخبرنا أحمد بن عثمان بن حكيم قال حدثنا أبي أنبأنا الحسن وهو ابن صالح عن أبي إسحق ح و حدثنا عمرو بن علي قال حدثنا عبد الرحمن قال حدثنا شريك عن أبي إسحق عن الأسود
كان رسول الله ﷺ لا يتوضأ بعد الغسل
No references are available.
[Hasan]. Recorded by Tirmidhi, Taharah, chapter on what has been said about wudu after ghusl, hadith no. 107, and by Ibn Majah, Taharah, chapter on wudu after ghusl, hadith no. 579, from the hadith of Sharik the judge, with this wording. It is also found in the Kubra, hadith no. 249, and Hakim graded it sahih, as did Dhahabi, as mentioned in Nayl Maqsud, hadith no. 250.Abu Ishaq stated explicitly that he heard it directly in some versions, and Ibn Sayyid Nas strengthened it. Tirmidhi said, hasan sahih.The hadith is found in Bayhaqi, 1/201, 202, and he himself graded it sahih, as did Ibn Hazm.