COVID-19 can lead to acute respiratory syndrome, which can be due to dysregulated immune signaling. We analyze the distribution of CpG dinucleotides, a pathogen-associated molecular pattern, in the SARS-CoV-2 genome. We characterize CpG content by a CpG force that accounts for statistical constraints acting on the genome at the nucleotidic and amino-acid levels. The CpG force, as the CpG content, is overall low compared to other pathogenic betacoronaviruses; however it widely fluctuates along the genome, with a particularly low value, comparable to the circulating seasonal HKU1, in the spike coding region and a greater value, comparable to SARS and MERS, in the highly expressed nucleocapside coding region (N ORF), whose transcripts are relatively abundant in the cytoplasm of infected cells and present in the 3’UTRs of all subgenomic RNA. This dual nature of CpG content could confer to SARS-CoV-2 the ability to avoid triggering pattern recognition receptors upon entry, while eliciting a stronger response during replication. We then investigate the evolution of synonymous mutations since the outbreak of the COVID-19 pandemic, finding a signature of CpG loss in regions with a greater CpG force. Sequence motifs preceding the CpG-loss-associated loci in the N ORF match recently identified binding patterns of the Zinc finger Anti-viral Protein. Using a model of the viral gene evolution under human host pressure, we find that synonymous mutations seem driven in the SARS-CoV-2 genome, and particularly in the N ORF, by the viral codon bias, the transition-transversion bias and the pressure to lower CpG content.