Private property is still "private" even if the public are invited to, from a technical perspective: that is, is still privately owned, and so any laws that only apply to publically (i.e. city, county, state, or federal government) owned property would not apply. However, many laws do not take cognizance of  who or what owns the property and rather instead look to the use, so that, for example, for purposes of anti-discrimination law, restaurants and movie theatres are considerecd places of public accomodation, even though they are privately owned. The public use, not the private ownership, is what counts for that purpose.Therefore, it is impossible to definitively answer your question without knowing the law under which you were being ticketed, so we can see to which property, defined in what fashion, it applies.