Ribonucleotides represent a threat to DNA genome stability and transmission. Two types of Ribonuclease H (RNase H) excise ribonucleotides when they form part of the DNA strand, or hydrolyse RNA when it base-pairs with DNA in structures termed R-loops. Loss of either RNase H is lethal in mammals, whereas yeast survives the absence of both enzymes. RNase H1 loss is tolerated by the parasite Trypanosoma brucei but no work has examined the function of RNase H2. Here we show that loss of T. brucei RNase H2 (TbRH2A) leads to growth and cell cycle arrest that is concomitant with accumulation of nuclear damage at sites of RNA polymerase (Pol) II transcription initiation, revealing a novel and critical role for RNase H2. Differential gene expression analysis reveals limited overall changes in RNA levels for RNA Pol II genes after TbRH2A loss, but increased perturbation of nucleotide metabolic genes. Finally, we show that TbRH2A loss causes R-loop and DNA damage accumulation in telomeric RNA Pol I transcription sites, also leading to altered gene expression. Thus, we demonstrate separation of function between two nuclear T. brucei RNase H enzymes during RNA Pol II transcription, but overlap in function during RNA Pol I-mediated gene expression during host immune evasion.