Can the property put stickers on the car in private?

No, the property does not belong to the state administrative organs and has no right to impose penalties and fines on illegal acts. Only the state administrative organs have the right to punish.

Legal basis:

Article 942 of the Civil Code of People's Republic of China (PRC) * * * Property service providers shall, in accordance with the agreement and the nature of the use of the property, properly repair, maintain, clean, afforest and manage some owners in the property service area, maintain the basic order of the property service area, and take reasonable measures to protect the personal and property safety of the owners.