  Context. A necessary ingredient in understanding the star formation history
of a young cluster is knowledge of the extinction towards the region. This has
typically been done by making use of the colour-difference method with
photometry, or similar methods utilising the colour-colour diagram. Aims. The
colour-excess can be independently determined by studying the decrements of the
recombination lines produced by the nebular gas. Having access to many
recombination lines from the same spectral series removes the need of adopting
an extinction curve. Methods. Using the Micro-Shutter Assembly (MSA) on board
the Near InfraRed Spectrograph (NIRSpec), multi-object spectroscopy was
performed, yielding 600 nebular spectra from the Galactic massive star
formation region NGC 3603. The recombination line intensity ratios were used to
determine independent values of colour-excess. Results. The extinction
characteristics of NGC 3603 are similar to other Galactic HII regions like
Orion, as well as starburst regions such 30 Doradus in the Large Magellanic
Cloud, in that we find a relatively large value of total-to-selective
extinction of 4.8 $\pm$ 1.06, larger than the Galactic average of 3.1. We find
a typical value for the colour-excess of 0.64 $\pm$ 0.27, significantly lower
than values determined in previous studies. We also present a stacked nebular
spectrum with a typical continuum S/N = 70. This spectrum highlights the
recombination lines of the HII region, several s-process elements such as Kr
III and Se IV, and molecular H2 emission lines. Conclusions. Using ratios of
hydrogen recombination lines, we calculated the total-to-selective extinction,
colour-excess and visual extinction for > 200 lines of sight across NGC 3603.
An extinction curve with a total-to-selective extinction of 4.8 $\pm$ 1.06 was
found, corresponding to a colour-excess of 0.64 $\pm$ 0.27.
