We present wide-field, spatially and highly resolved spectroscopic observations of Balmer filaments in the northeastern rim of Tycho's supernova remnant in order to investigate the signal of cosmic-ray (CR) acceleration. The spectra of Balmer-dominated shocks (BDSs) have characteristic narrow (FWHM ~ 10 km s-1) and broad (FWHM ~ 1000 km s-1) Hα components. CRs affect the Hα-line parameters: heating the cold neutrals in the interstellar medium results in broadening of the narrow Hα-line width beyond 20 km s-1, but also in reduction of the broad Hα-line width due to energy being removed from the protons in the post-shock region. For the first time we show that the width of the narrow Hα line, much larger than 20 km s-1, is not a resolution or geometric effect nor a spurious result of a neglected intermediate (FWHM ~ 100 km s-1) component resulting from hydrogen atoms undergoing charge exchange with warm protons in the broad-neutral precursor. Moreover, we show that a narrow line width >> 20 km s-1 extends across the entire NE rim, implying CR acceleration is ubiquitous, and making it possible to relate its strength to locally varying shock conditions. Finally, we find several locations along the rim, where spectra are significantly better explained (based on Bayesian evidence) by inclusion of the intermediate component, with a width of 180 km s-1 on average.