LoD2 models include roof shapes and thus provide added value over their LoD1 counterparts for some applications such as estimating the solar potential of rooftops. However, because of laborious acquisition workflows they are more difficult to obtain than LoD1 models and are thus less prevalent in practice. This paper explores whether the type of the roof of a building can be inferred from semantic LoD1 data, potentially leading to their free upgrade to LoD2, in a broader context of a workflow for their generation without aerial campaigns. Inferring rooftop information has also other uses: quality evaluation and verification of existing data, supporting roof reconstruction, and enriching LoD0/LoD1 data with the attribute of the roof type. We test a random forest classifier that analyses several attributes of buildings predicting the type of the roof. Experiments carried out on the 3D city model of Hamburg using 12 attributes achieve an accuracy of 85% in identifying the roof type from sparse data using a multiclass classification. The performance of binary classification hits the roof: 92% accuracy in predicting whether a roof is flat or not. It turns out that the two most useful variables are footprint area and building height (i.e. LoD1 models without any semantics, or LoD0 with such information), and using only them also yields relatively accurate results.