<p>Holomorphic diffeomorphism anomalies of 2 <i>n</i>-dimensional gravitational theories in Beltrami parametrisation (Kodaira-Spencer anomalies) are computed in the <span>brst</span> framework, using an extension of the Stora-Zumino method. This method, which allows to compute anomalies in a very concise way, makes manifest the topological origin of anomalies. They have a clear geometric interpretation, since they are expressed in terms of Chern polynomials and Pontryagin invariants. The key ingredient is the formulation of the <span>brst</span> transformations in terms of polyforms, whose total degree is the sum of the form degree and of the ghost number. This approach simplifies significantly the analysis available in literature and it allows to compute many other solutions. Namely, an anomaly, which was computed using different methods, is proved to be a consistent <span>brst</span> anomaly, thereby supplementing a conclusion in a previous analysis.</p>