The closest reference that I can find to this question is from Vachanamrut. In Vadatal prakaran, Lord Swaminarayan answering to sadhu’s question says
The two types of bodies, sthul and sukshma, are both intimately associated with the kāran body in the same way that a tree is intimately associated with its seed. That is why it is called the kāran body. This kāran body is a form of avidyā; it is without a beginning; and it retains its sanchit karmas.
So there are definitely scriptural basis to the karma retained/stored in Sukshma and karan shareer.
In case anyone not aware, Swaminarayan followed the Vishishtadvait philosophy of Ramanujacharya and frequently quoted verses and references from Upanishads (although not specifically mentioned in this chapter “)
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Here are some more references to related topic. It provides scripture reference about “information on residual karma karma associated with jiva (carry/retain/store for the lack of better word)
From Āpastamba-Dharmasūtra, 2-2-3
Then, on returning to this world, he obtains, by virtue of the remainder of merit, birth in a distinguished family.........
Above verse tells that there Exists Information (stored or retained) on residual karma (like Sanchit) and which is related to Jiva returning to this world (which may be in Jiva in sukshma or karana shareer)
(More reference to residual karma associated to jiva are in Shankaracharya commentary here on Taittireya Upanishad
Please also see chapter on Brahmvidya
(I have been researching on same topic so I wanted to share my notes. Everyone is welcome to edit the answer)