Yes, there is some overlap. But K really knew very little about Nagarjuna - he famously didn’t read religious or philosophical books (apart from some poetic Buddhist literature when he was a young man), and so only picked up bits and pieces from others around him. He liked Nagarjuna’s passion for negation, but K’s mind was a million miles away from the rationally ascetic logical mind of Nagarjuna.
For instance, the orthodox way of interpreting Nagarjuna in Tibet (which takes its cue from Tsongkhapa) presents a very different kind of ‘emptiness’ from the more mystical or experiential variety of emptiness that K seems to have talked about. And with respect to their approaches to thought, thinking - as I pointed out earlier - Nagarjuna (like Kant, in this regard) was interested in what (logical) thought does (when faced by its conceptual objects); while Krishnamurti was more interested in what thought is in itself, how it comes about, what it is made of (physically), what it does to us psychologically (creating psychological time, fear, desire, suffering, etc).
In fact, I would argue that K had more in common with an almost completely unknown early Buddhist - called Maha Kaccana - than with Nagarjuna! Listen to the following, and let me know if you see the resemblance.
Evidence for the striking similarity of (parts of) K’s teaching can be found in a passage from the Madhupindika Sutta, which is attributed to a Buddhist teacher called Maha Kaccana (a disciple of the Buddha). It states that, following the contact of the eye with the object seen, “there is sensation”. Then:
what one senses one apperceives, what one apperceives one thinks over, what one thinks over one conceptually proliferates; because of which conceptual proliferation, apperception and reckoning afflict a person, with regard to (all) forms, of the past, future and present.
That is: in this text Maha Kaccana clearly distinguishes sensation (and the feeling it gives rise to in the body) from thinking; and correlates this thinking (“conceptual proliferation”) with the experience of psychological time (“the past, future and present”) - aka what K sometimes called thought-time - which engenders suffering (“affliction”).
Some early Buddhists (and probably most Buddhists even today) believed that the cause of suffering was in the senses (causing tanha, thirst); but here Maha Kaccana very clearly shows how the cause of suffering is rather in our cognitive faculty, our thinking (when it is dominated by avidya, a lack of awareness).
K’s approach is very much in keeping with this perspective (see, for instance, how K describes the coming into being of desire from thought entering into sensation and giving it a temporal continuity, etc which leads to suffering).