Under our current legal system, the laws aren't really set up to address the problem of a person with health condition coughing on another person. That said, there are some ways a prosecuting attorney might address the issue.
I should note that during the Spanish Flu (that took the lives of 600,000 Americans) most cities had laws on the books the made it a crime to spit or to cough or sneeze without using a handkerchief. In New York City many theaters were allowed to remain open during the Spanish Flu. The theater manager would address the crowd before the film about the rules for coughing. Today, the dangers of coughing haven't been highlighted as much, but the CDC has now conceded that the public could benefit from the use of masks. However, under the current state of the law in Washington, there are no laws that really govern coughing or sneezing in public. We do have the catch-all statute of Reckless Endangerment so let's talk about that and then we will shift to instances where people cough on another person to try intentionally to scare them.
Reckless Endangerment
Under Washington law, Reckless Endangerment is defined as a reckless act that creates "a substantial risk of death or serious physical injury to another person." There aren't a lot of legal precedents where people have been charged under this statute. During the A.I.D.S. epidemic, there were instances where individuals were charged with attempted murder for engaging in sexual relations, but HIV had a much higher fatality rate than what we are facing currently. There are some precedents for reckless endangerment charges for exposing someone to hepatitis or herpes, but such charges are almost always in the context of sexual relations. There just aren't any precedents that would support reckless endangerment charges for coughing on or near another person.
Intentionally Coughing on Someone in Washington State
Under Washington law, an assault is a "harmful or offensive" touching. Under this definition, spitting qualifies as a "touching" (See State v. Hall) but it is not clear if coughing would be an assault. There just isn't any sort of direct contact that is made with coughing. It is hard to prove that the defendant had any sort of disease, much less that it was his intent to infect someone. There is the argument that an assault can occur by the simple apprehension of harm. In other words if a person acts with an "intent to create in another an apprehension and fear of bodily injury" that could count as an assault. The problem is the "intentional cougher" must inform the would be victim that he or she has the coronavirus. Merely coughing at someone in general is certainly rude, but it is unlikely to sustain a criminal conviction. This seems to be the possible missing element in the recent arrest of Spokane resident Tanner Macri, who the police alleged "coughed in their face" when they went to arrest his sister, Shayden Macri. Tanner Macri never claimed to have the virus (as this guy or this guy allegedly did). Even if a cougher is sick, it must be proved beyond a reasonable doubt that it was his intent to be taken seriously. We are still at the front end of this health crisis, and there are not established norms for behavior on this subject. Additionally, these coughers will ultimately by judge by a jury of their peers, and, let's face it, the country is extremely divided on their perceptions of this virus. This is not to say that the people should have a sense of humor about being coughed on, my point is that this is an area of the law that the legislature needs to address. The ambiguity in the law is probably why during the Spanish Flu many cities simply mandated the use of handkerchiefs, i.e. to remove any gray area.
For more information on the law in general, see out page on assault.