I don't know of such a study.
I looked at Wikipedia to learn the first thing about that Gita:
Ashtavakra Gita is a dialogue between Ashtavakra and Janaka on the nature of soul, reality and bondage.[9] It offers a radical version of non-dualistic philosophy. The Gita insists on the complete unreality of external world and absolute oneness of existence. It does not mention any morality or duties, and therefore is seen by commentators as 'godless'. It also dismisses names and forms as unreal and a sign of ignorance.[10]
In a conversation between Janaka and Ashtavakra, pertaining to the deformity of his crooked body, Ashtavakra explains that the size of a Temple is not affected by how it is shaped, and the shape of his own body does not affect himself (or Atman). The ignorant man's vision is shrouded by names and forms, but a wise man sees only himself:[11][12]
You are really unbound and action-less, self-illuminating and spotless already. The cause of your bondage is that you are still resorting to stilling the mind. (I.15)
You are unconditioned and changeless, formless and immovable, unfathomable awareness, imperturbable- such consciousness is un-clinging. (I.17)
You are not bound by anything. What does a pure person like you need to renounce? Putting the complex organism to rest, you can go to your rest. (V.1) [13]
The Pali suttas avoid saying "you are" and "I am" and so on -- the Buddhist doctrine is called "Anatta" or "Anatman", contrasted with the Vedic doctrine of "Atman".
I did a quick Google search and the first thing I found was ...
Ashtavakra Gita. One of the great spiritual texts of ancient India. Liberation is the priority…
... which is a little blog entry, not a study. The author doesn't say much (it's short) except recommends reading the Gita. The one thing he does say -- referring to "the language of ‘I’ and ‘Self’" that's used in the Gita -- is ...
Yes, the words in places are certainly different from the Buddha-Dharma. That is hair-splitting, a formation of an unnecessary duality.
... so I guess maybe he recognises that it sounds a bit heretical or counterfactual to an orthodox early-Buddhist view.
One time that author (i.e. Christopher Titmuss) was quoted previously on this site was actually on a similar topic -- Was the doctrine of 'Anatta', accepted as doctrine by modern Buddhism, actually taught by the Buddha? -- i.e. where someone questioned something he had written about Anatta, and questioned whether that matches an orthodox Buddhist view or doctrine.
If you're interested you might also see this topic -- How is it wrong to believe that a self exists, or that it doesn't? -- which focuses on the sutta which was alluded to in the previous topic above.
If you like the format of the Gita (i.e. question-and-answer) then you might possibly like The Questions of King Milinda e.g. summarised here. They include a famous "simile of a chariot", which explains that there isn't really a "self" in the same way that there isn't really a "chariot". I found that explanation a bit abstract (i.e. just words) and I prefer the doctrine in MN 22, which also has some famous similes, but especially the explanation of views-of-self which includes the following as a reason for not having a doctrine-of-self,
Mendicants, it would make sense to be possessive about something that’s permanent, everlasting, eternal, imperishable, and will last forever and ever. But do you see any such possession?” “No, sir.” “Good, mendicants! I also can’t see any such possession.
It would make sense to grasp at a doctrine of self that didn’t give rise to sorrow, lamentation, pain, sadness, and distress. But do you see any such doctrine of self?” “No, sir.” “Good, mendicants! I also can’t see any such doctrine of self.
... but maybe it's necessary that there are several explanations (about self and selfishness and so on).
Two more things I'd like to mention.
One is that the bits of the Gita which Wikipedia quotes, above, remind of Huineng's poem -- contrast the Gita's saying,
You are really unbound and action-less, self-illuminating and spotless already
... with Huineng's saying, I think, effectively,
There is no "you".
The other thing is that items listed in Christopher Titmuss' blog, e.g. ...
- Can the water in the wave be separate from the Ocean?
- Can the cloud be separated from the Sky?
- Can a human being exist separate from the environment?
- Is there the capacity to embrace separation and non-separation?
... seem to me to be, as Andrei's answer said, "in-line with the teaching of Mahayana Buddhism" -- i.e. they're examples of a doctrine of "emptiness" (sunyata), more than of "non-self" (anatta).
Perhaps it would be interesting to compare it in detail with Buddhist doctrine, but like I said I don't know of such. There probably are similarities and differences, and I guess it's up to you to decide whether. like Christopher Titmuss, you consider such differences to be "hair-splitting".
If I read it one of the first things I read is ...
Liberation is to know yourself
as Awareness alone
I think that "awareness" there might mean what Buddhism calls consciousness rather than mindfulness; but to me that (i.e. "know yourself as Awareness") sounds contrary to elementary Buddhist doctrine: which says that consciousness is impermanent and dependently originated (e.g. it varies depending on "contact"), and that therefore you shouldn't identify with it and so on.
I don't want to disparage it, so I don't want to go on pointing out disparities.
Maybe the doctrine-of-self is important though: according to the Buddhism of the Pali suttas abandoning the "self-view" (or "self-doctrine" or "identity-view") is a milestone, the first stage of enlightenment.
Anyway I think that comparative-religion topics on this site are meant to be introductions to Buddhism, maybe this answer does that. I don't know though, what do you already know about Buddhism, you didn't mention that in the question.
A quick scan suggests that some of its themes are like the Buddhism of the Pali suttas -- e.g. that desire is tedious, that attachment has been going on since forever and that it's time to stop, that ignorance is a problem. It also has some themes that may be reminiscent of later versions of Buddhism , e.g. ...
Right and wrong, pleasure and pain,
exist in mind only.
They are not your concern.
... which might sound a bit scandalous to someone who's used to early Buddhism's including/emphasising ethics in its doctrine (you might see e.g. Can you criticise or improve Ven. Bodhi's description of Mahayana for more on that topic).
