According to The Cultural Heritage of India, Vol. II, the Aṣṭāvakra Gītā a.k.a Aṣṭāvakra Saṃhitā is an independent work. It doesn't belong to any known epic or Purāṇa.
IMITATIONS OF THE BHAGAVAD-GĪTĀ AND LATER GĪTĀ LITERATURE
EXTENT AND NATURE
Besides the Bhagavad-Gītā, which is generally known as 'the Gītā',
scholars have noticed many other tracts of varying lengths composed in
verse form to which the title 'Gītā' is given. Sixteen of them are
from (a) the Mahābhārata, twenty from (b) the Purāṇas and similar
treatises, and four (c) found as independent works untraced to any
other known epic or Purāṇa.
Under the group marked (a) are to be found: Utathya-Gītā,
Vāmadeva-Gītā, Ṛṣabha-Gītā, Ṣaḍaja-Gītā, Sampāka-Gītā, Maṅki-Gītā,
Bodhya-Gītā, Vicakhnu-Gītā, Hārīta-Gītā, Vṛtra-Gītā, Parāśara-Gītā,
Haṃsa-Gītā, Brahma-Gītā, Anu-Gītā and Brāhmaṇa-Gītā.
In the group marked (b) are included: two Kapila-Gītās, Haṃsa-Gītā,
Bhikṣu-Gītā, Devī-Gītā, Gaṇeśa-Gītā, two Brahma-Gītās, Sūta-Gītā,
three Yama-Gītās, Śiva-Gītā, two Rāma-Gītās, Sūrya-Gītā and
Vasiṣṭha-Gītā.
Under the group marked (c) come four works: Aṣṭāvakra-Gītā,
Avadhūta-Gītā, Uttara-Gītā, and Pāṇḍava-Gītā.
The names Īśvara-Gītā, Haṃsa-Gītā and Vyāsa-Gītā in all probability
refer to the Bhagavad-Gītā only and no other work.