Possibly because God is rarely seen as directly interfering in worldly matters (He rather uses karman to do it), I am not aware of philosophical discussions about whether human beings alone are responsible of good and evil or God is corresponsible as well, insofar as He favours the first and lets the latter happen. One also does not find the kind of reflections one finds in Islamic thought, asking why God does not let future evil-doers die while they are still harmless children, in order to prevent them from doing evil and, hence, to eternally suffer in hell... Nor does one find the problem of the coexistence of God's goodness and free will. I tend to think that the Christian answer to this problem would be that free will is so precious, that God prefers people to be free rather than forcing them to be good. This might be due to the fact that God himself wants to be chosen freely and freely loved. But one might object that this desire of Him implies that there are also evil-doers, who might harm other people. How can one justify a desire, if this indirectly implies harming others?
Mīmāṃsā authors deny any role to god as a philosophical entity. They may personally adore a personal God, but tend to be quite strict in denying to Him/Her any ontological foundation. In other words, god has no place as a justification for the system and there is, consequently, no need to discuss one's freedom in respect to his omnipotence. The absence of any comparison with god also entails that Mīmāṃsā authors do not need to specify in which sense one can be said to be free, given that one is not as free as god is, since, for instance, god can assume every possible form and we cannot. (Pratyabhijñā authors, in this connection, suggest that the limited subjects only enjoy a fraction of the God's infinite power of freedom.)
Are you aware of discussions about God and free will in Sanskrit texts?
On free will in Mīmāṃsā, see this post.
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