We study the evolved stellar population of the galaxy Sextans A. This galaxy is one of the lowest metallicity dwarfs in which variable asymptotic giant branch stars have been detected, suggesting that little metal enrichment took place during the past history. The analysis consists in the characterization of a sample of evolved stars, based on evolutionary tracks of asymptotic giant branch and red supergiant stars, which include the description of dust formation in their winds. Use of mid-infrared and near-infrared data allowed us to identify carbon-rich sources, stars undergoing hot bottom burning, and red supergiants. The dust production rate, estimated as 6 × 10-7M⊙/yr, is dominated by ˜10 carbon stars, with a small contribution of higher mass M-stars, of the order of 4 × 10-8M⊙/yr. The importance of this study to understand how dust production works in metal-poor environments is also evaluated.