Vedanta philosophy states that samâdhi is obtained by realising one's identity with the soul(âtman) separate from the body & mind. Tantra philosophy, though not denying the existence of âtman states that samâdhi is obtained by the ascent of the Kundalinî to Sahasrâra-chakra. How can the âtman be related to Kundalinî ?
Both Kuņdalini and Ātman are small words for a large world!
The Awakning of kuņdalini from a Dormant state into the form of conscious power and the consequent transmutation of Jīva into śiva, followed by their Joyous unification in the self Delight of Brahma, are duly recognized in Tantras. (Foreword Sarvollāsatantram by M.M.Gopinath)
Immediately, the question arises what is Jīva? What is śiva? Kulavarna tantra says:
(कुलार्णवतन्त्रम्)- देहो देवालयो देवि जीवो देवः सदाशिवः । त्यजेदज्ञाननिर्माल्य सोऽहम्भावेन पूजयेत् ॥
Lord shiva says 'O devi Parvati' This body (देह) is itself the Devālay (देवालय)! It consists of a God called 'jivā' (जीव). Shastra calls this (सदाशिव) sadāshivā! It has been covered with lack of knowledge, the jiva's responsiblity is to remove this cover & worship it with 'sohām bhāva'.
(ज्ञान संकूलितन्त्रम्)- शरीरञ्चैवमात्मानमन्तरात्मा मनो भवेत् । परमात्मा भवेच्छून्यं मनो यत्र विलीयत ॥
The Gaayn Sankuli says: This body (देह) is the Ātman, the mind (मन) is AntarĀtman and the void is ParamĀtman. Void is the place where the mind merges into.
So, The God called jiva that resides in this body transforms to the Siva due to the Awakening of the Kuņdalini and its unification within the Sahashara. The Ātman as body itself would experience the same. While the AntarĀtman would transit into the void.
The Kuņdalini shakti stays in the Muladhara Chakra, from where it rises and moves through each subsequent chakra. The Kaankalmalini Tantra explains how that 'Kuņdalini' must be taken from the Muladhara to the Sahasrara.
During the transit of Kundalini from the Svadhishthana to the Anahata the 'JivaAtman' becomes as if Kuņdalini-
जीवात्मानं कुण्डलिनीं रसञ्च मणीपूरके ।
Take that 'Rasa' (?) from the second chakra (Svadhishthana) to the Manipur along with the Kuņdalini in the form of JivaAtma.
तत्र चक्षूरिन्द्रियञ्च कृत्वा तेजोमयं यजेत्। एतं रसञ्च सुभगे रुपे नीत्वा महाभगे॥५३॥
Then take the 'Rasa' (from Svadhishthana) mixing it with the 'Rupa' (?), into the Anahata Chakra.
जवीवात्मानं कुण्डलिनी रुपचानाहते नयेतु । बन्धूकपुष्पसंगशं तत्पद्म द्वादशारकम् ॥५४॥
Then bring Kuņdalini in the form of JivaAtman into the Anahata Chakra.
कादिठान्तैः स्फुरद्वर्णो: शोभितां हरवल्लभाम् । तत्कणिकाया वायुच्ञाजीवस्थान निवासिनम् ॥५५॥
In the 'Karnika' (the pericarp of lotus?) of the Anahata Chakra lies the 'vayu' which resides in the 'JeevSthan'. This Chakra is present in the heart. The Gautami Tantra says,
गौतमीये-- इज्यमानो हृदात्मायं हृदये स्थाच्चिदात्मन: ।क्रियते तत्परत्वं तु हन्मनत्रेण ततः परम् ॥१॥
The Atma reside in the Heart, thus then perform the Nyasam with 'Namha'.
Thus, Kuņdalini and the Atma are viewed entirely distinct. However, during the rise of Kuņdalini form the Svadhishthana to the Anahat chakra one needs to recognize the jeevatma in the form of Kuņdalini. Which is taken into the Heart (Anahat chakra) where the Atman resides. The Anahata chakra is indeed of the Vyau Tatva. In samadhi, there would be no distinction between Atma, JeevAtma, or the Kuņdalini.
Note: There might exist variety of perspectives in which one can answer. There are lot of concepts that are taking part in question, I tried my best to explain. However as one might see, there is not a very direct corrlection between Atma and Kundalini. This was all what I could get to.