Many agencies release datasets and statistics about groups of individuals that are used as input to a number of critical decision processes. To conform with privacy requirements, these agencies are often required to release privacy-preserving versions of the data. This paper studies the release of differentially private datasets and analyzes their impact on some critical resource allocation tasks under a fairness perspective. The paper shows that, when the decisions take as input differentially private data, the noise added to achieve privacy disproportionately impacts some groups over others. The paper analyzes the reasons for these disproportionate impacts and proposes guidelines to mitigate these effects in the full version of this work. The proposed approaches are evaluated on critical decision problems that use differentially private census data.