"Of 49 patients with mild symptoms of Covid-19 in three hospitals in southern Asian countries, only two had low levels of vitamin D; of 104 patients with critical or severe symptoms, only four did not have low levels of vitamin D." https://www.telegraph.co.uk/news/2020/05/03/time-take-seriou...
"The VDI (Vitamin D Insufficiency) prevalence in ICU patients was 84.6%, vs. 57.1% in floor patients. Strikingly, 100% of ICU patients less than 75 years old had VDI. Coagulopathy was present in 62.5% of ICU COVID-19 patients, and 92.3% were lymphocytopenic. Conclusions: VDI is highly prevalent in severe COVID-19 patients" https://www.medrxiv.org/content/10.1101/2020.04.24.20075838v...
"Vitamin D has been shown to have an anticoagulant effect. A decrease in 25-hydroxyvitamin D [25(OH)D] concentration has also been associated with an increased risk of venous thromboembolism. " https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4069050/
There is also other literature suggesting that Vitamin D can reduce the risk for the "cytokine storm" which leads to acute respiratory distress syndrome by reducing the production of pro-inflammatory cytokines (while increasing the expression of anti-inflammatory cytokines). Again, I'm not a doctor but supplementation is likely to be fairly low risk. There is increasing evidence that there's some sort of correlation and it may be worth exploring.