I am looking for references on the story of Sri Krishna saving Parikshith. Specifically looking for references to section where Sri Krishna is said to have touched the charred body of the baby, vowing to his brahmacharya and truthfullness.
The details is mentioned in many chapter of Mahabharata and Bhagavata Purana but as you are "specifically looking for references to section where Sri Krishna is said to have touched the charred body of the baby, vowing to his brahmacharya and truthfullness", I think you are looking for passage from Mahabharata: Aswamedha Parva: Anugita Parva: Section LXIX:
That foremost of beings, hearing those heart-rending lamentations of hers, touched water and withdrew the (force of the) Brahma-weapon.1 That hero of unfading glory, belonging to the race of the Dasarhas, promised to give the child his life. Then he of pure soul, said these words in the hearing of the whole universe,--'O Uttara, I never utter an untruth. My words will prove true. I shall revive this child in the presence of all creatures. Never before have I uttered an untruth even in jest. Never have I turned back from battle. (By the merit of those acts) let this child revive! As righteousness is dear to me, as Brahmanas are specially dear to me, (by the merit of that disposition of mine) let Abhimanyu's son, who is born dead, revive! Never hath a misunderstanding arisen between me and my friend Vijaya. Let this dead child revive by that truth! As truth and righteousness are always established in me, let this dead child of Abhimanyu revive (by the merit of these)! As Kansa and Kesi have been righteously slain by me, let this child revive today by that truth!' After these words were uttered by Vasudeva, that child, O foremost one of Bharata's race, became animate and began gradually to move, O monarch.'
You can find the story in Skanda 1 chapter 8 in the Bhagavata purana
However this is not in great detail, Mahabharata may have description in greater detail.