We present intermediate-resolution (R$sim$1000) spectra in the $sim$3500-10,000 A range of 14 globular clusters in the magellanic irregular galaxy NGC 4449 acquired with the Multi Object Double Spectrograph on the Large Binocular Telescope. We derived Lick indices in the optical and the CaII-triplet index in the near-infrared in order to infer the clusters stellar population properties. The inferred cluster ages are typically older than $sim$9 Gyr, although ages are derived with large uncertainties. The clusters exhibit intermediate metallicities, in the range $-1.2lesssim$[Fe/H]$lesssim-0.7$, and typically sub-solar [$alpha/Fe$] ratios, with a peak at $sim-0.4$. These properties suggest that i) during the first few Gyrs NGC 4449 formed stars slowly and inefficiently, with galactic winds having possibly contributed to the expulsion of the $alpha$-elements, and ii) globular clusters in NGC 4449 formed relatively late, from a medium already enriched in the products of type Ia supernovae. The majority of clusters appear also under-abundant in CN compared to Milky Way halo globular clusters, perhaps because of the lack of a conspicuous N-enriched, second-generation of stars like that observed in Galactic globular clusters. Using the cluster velocities, we infer the dynamical mass of NGC 4449 inside 2.88 kpc to be M($<$2.88 kpc)=$3.15^{+3.16}_{-0.75} times 10^9~M_odot$. We also report the serendipitous discovery of a planetary nebula within one of the targeted clusters, a rather rare event.