Context. NGC 5253 is a nearby peculiar blue compact dwarf (BCD) galaxy that, on account of its proximity, provides an ideal laboratory for detailed spatial study of starburst galaxies. An open issue not addressed so far is how the collisional and self-absorption effects on He I emission influence the determination of the He+ abundance in 2D and what is the relation to the physical and chemical properties of the ionised gas. Aims. A 2D, imaging spectroscopy, study of the spatial behaviour of collisional and radiative transfer effects in He+ and their impact on the determination of He+ abundance is presented for the first time in a starburst galaxy. Methods. The He I lines were analysed based on previously presented integral field spectroscopy (IFS) data, obtained with FLAMES at the VLT and lower resolution gratings of the Giraffe spectrograph, as well as with GMOS at Gemini and the R381 grating. Results. Collisional effects reproduce the electron density (ne) structure. They are negligible (i.e. similar to 0.1-0.6%) for transitions in the singlet cascade but relatively important for those in the triplet cascade. In particular, they can contribute up to 20% of the flux in the He I/l7065 line. Radiative transfer effects are important over an extended and circular area of similar to 30 pc in diameter centred on the super star clusters (SSCs). The singly ionised helium abundance, y(+), has been mapped using extinction-corrected fluxes of six He I lines, realistic assumptions for electron temperature (T-e), n(e), and the stellar absorption equivalent width, as well as the most recent emissivities. We find a mean(+/- standard deviation) of 10(3) y(+) similar to 80.3(+/-2.7) over the mapped area. The relation between the excitation and the total helium abundance, y(tot), is consistent with no abundance gradient. Uncertainties in the derivation of helium abundances are dominated by the adopted assumptions. We illustrate the difficulty of detecting a putative helium enrichment owing to the presence of Wolf-Rayet (WR) stars in the main GH IIR. Data are marginally consistent with an excess in the N/He ratio in the nitrogen-enriched area. This excess would be close to both the atmospheric N/He ratios in WR stars and the uncertainties estimated for the N/He ratios. We explored the influence of the kinematics in the evaluation of the He I radiative transfer effects. Our data empirically support the use of the traditional assumption that motions in an extragalactic H II region have a negligible effect in the estimation of the global optical depths. Individually, the broad kinematic component (associated with an outflow) is affected by radiative transfer effects in a much more significant way than the narrow one. We find a relation between the amount of extra nitrogen and the upper limit of the contribution from radiative transfer effects that requires further investigation. We suggest that the electron temperature could be a common agent causing this relation.
