The paint was dripping from many of the rocks around the scenic falls, he said.
The investigation was prompted by a seasonal employee who reported it over the weekend.
The graffiti remains up for now, and he did not know when the park was planning to clean it up or how long such work might take.
An employee at Rocks State Park's main phone number said the park manager, who would be the only one to comment on it, would not be available until Tuesday.
Police had no suspects in the case as of Thursday. They are asking anyone with information to call the Natural Resources Police' Gwynnbrook office, 1-800-628-9944, or NRP's 24-hour dispatch, 410-260-8888.