Quite a few states have laws against things like "interfering with a peace officer" or "obstructing a peace officer".
This action might or might not fall within that statute, but there's enough variation in wording between states that it's impossible to say in general. It can also depend on some other parts of the situation, such as whether the police officer in question is busy doing something else at at the time or not.
In particular some states' laws include wording about the obstruction involving violence toward the peace officer, such as (Colorado):
A person commits obstructing a peace officer, firefighter, emergency medical services provider, rescue specialist, or volunteer when, by using or threatening to use violence, force, physical interference, or an obstacle, such person knowingly obstructs, impairs, or hinders the enforcement of the penal law or the preservation of the peace by a peace officer, acting under color of his or her official authority;
So, in Colorado the judge/jury would have to decide whether (for example) your action could be construed as creating/using an obstacle to the police officer performing his duty.
In Illinois, however, the law doesn't include similar language limiting such obstruction to things like violence:
A person who knowingly resists or obstructs the performance by one known to the person to be a peace officer, firefighter, or correctional institution employee of any authorized act within his or her official capacity commits a Class A misdemeanor.
So, in Illinois, there's a lot better chance that you could be convicted, even though your action was relatively indirect and non-violent.
In at least some states, the act of running away has been ruled sufficient to qualify as obstruction but at least as far as I can see, it's usually running away when an officer has approached that person. For example, Nebraska law uses the wording:
A person commits the offense of obstructing a peace officer, when, by using or threatening to use violence, force, physical interference, or obstacle, he or she intentionally obstructs, impairs, or hinders (a) the enforcement of the penal law or the preservation of the peace by a peace officer or judge acting under color of his or her official authority or (b) a police animal assisting a peace officer acting pursuant to the peace officer's official authority.
However, Corey Richter was convicted of violating this law based only on running away from the police:
Richter had been staying with his grandmother who, on October 20, 1986, asked the police to remove him from her home. Officers Mike Brunz and Douglas French, both in uniform, went to the grandmother's home in a marked police car to so do. As they approached the home, they could hear Richter arguing with and cursing and yelling at his mother. Officer French told Richter they were going to take him to a youth shelter for the evening. Richter ran away as the officers were escorting him to their automobile. Officer French then pursued Richter on foot, but lost sight of him. The officers found Richter approximately an hour later near his grandmother's home. Upon seeing the officers Richter started to flee again, but returned peacefully after his mother yelled for him to stop. No physical restraints were ever placed on Richter, nor did Richter ever resort to force.
[Ruling on appeal]
I'd rate it as extremely risky at best. At best, you'd probably be arrested and spend a few days/nights in jail, but not convicted. On the other hand, it could pretty easily result in a conviction, and the fact that the state's law has wording about using violence (or similar) wouldn't necessarily provide you with any protection.
