There is no clear evidence - we simply don't know.
Harm Pinkster (Pinkster 2015) writes that even though there may have been something comparable to the falling or rising tone known from many languages, including English,
we are not able to recover much information about Latin intonation (p. 15).
Pinkster mentions (in a footnote) that ancient grammarians and rhetoricians were interested in intonation (vox) but, as Hannah Rosen observes, "it it scarcely possible to describe them lucidly" (Rosen 2009: 337). Here are some examples she cites:
"Vocis mutationes totidem sunt quot animorum" (Cicero, Orator, 55)
"Quare, et quia nemo de ea re diligenter scripsit—nam omnes vix posse putarunt de voce et vultu et gestu dilucide scribi, cum eae res ad sensus nostros pertinerent—et quia magnopere ea pars a nobis ad dicendum conparanda est, non neglegenter videtur tota res consideranda." (Rhetorica ad Herennium, 3,19)
Here's a very revealing passage (Rhetorica ad Herennium, 4,54) illustrating their attitude towards serious study of intonation:
Pinkster, Harm. 2015. The Oxford Latin syntax. Volume 1: The simple clause. Oxford: Oxford University Press. (highly recommend - the best Latin grammar!)
Rosen, Hannah. 2009. Coherence, sentence modification, and sentence-part modification - the contribution of particles. In Baldi, Philip, and Pierluigi Cuzzolin, eds., New perspectives on historical Latin syntax. Volume 1. Syntax of the sentence, pp. 317-442. Berlin: Mouton de Gruyter.