To Kant, if you stop looking at something or if there are no agents with categories or elements of the understanding within the proximity of an object, does the noumenon manifest itself?
For Kant, a tree falling in a forest will make a sound in so far as every necessary condition for it making a sound has been given. In the Critique of Pure Reason, he generally extends both causality and the principle of sufficient reason to all possible experience (A195/B240  and A201/B246 )[*] such that, for any possible event, it's conditions to occur must have been given in the world. He also took causality for granted on a fragment  dating to 1788, immediatelly after the publication of the second edition of the CPR.
Now, compare the problem of a falling tree with Hume's problem of whether the sun will rise tomorrow given that it has risen every single day before. For Hume, our expectation that it ought to rise is completely due to our generalization of the past experience. For Kant, if the sun happens to not rise one morning, it should very well have a darn good reason not to, because otherwise such an event would violate those two principles.
On the other hand, it isn't impossible that a falling tree doesn't make a sound when no one is around for entirely empirical reasons but, just like it isn't impossible that the sun should explode overnight, we have no evidence to suggest that this is the case and thus we cannot think to ourselves that it might be without violating these principles, as whatsoever happens in the world ought to have a cause in the world. In anyway, the way this question is presented never suggests that humans ought to be considered a relevant empirical condition for it making a sound or not, but as a purely metaphysical question.
The bit about whether it makes a sound or not if no one has the relevant categories to perceive this event is a different question. Because, if the event in question isn't merely not perceived, but imperceptible, it wouldn't be an object in any possible experience and thus nothing could ever be said about it with any degree of certainty.
[*] With the caution of not extending their domain to the whole of experience, which would lead to the Third Antinomy of Pure Reason (A488/B516).
If, therefore, we experience that something happens, then we always presuppose that something else precedes it, which it follows in accordance with a rule.
 Kant, Immanuel. "Critique of Pure Reason". Cambridge University Press, 1998. p 308.
This rule for determining something with respect to its temporal sequence, however, is that in what precedes, the condition is to be encountered under which the occurrence always (i.e., necessarily) follows. Thus the principle of sufficient reasond is the ground of possible experience, namely the objective cognition of appearances with regard to their relation in the successive series of time
 Kant, Immanuel. "Critique of Pure Reason". Cambridge University Press, 1998. p 311.
Further, no alteration in the world (thus no beginning of that motion) can arise without being determined by causes in the world in accordance with laws of nature in general, thus not through freedom or a miracle proper;
 Kant, Immanuel. On Miracles. "Notes and fragments". Cambridge University Press, 2005. pp 290-291.
[...], if you assume that in everything that happens in the world there is nothing but a sequence occurring according to laws of nature, then the causality of the cause is always once again something that happens, and that necessitates your regress to still higher causes, and hence the prolonging of the series of conditions a parte priori without cessation. Mere efficient nature in the synthesis ofworld-events is thus too big for all your concepts.
If you choose now and then to admit occurrences produced from themselves, hence generated through freedom, then by an unavoidable law of nature the question "Why?" will pursue you, and require you, in accord with the causal laws of experience, to go beyond this point; then you will find that such a totality of connection is too small for your necessary empirical concept.
 Kant, Immanuel. "Critique of Pure Reason". Cambridge University Press, 1998. p 509.