They occurred between Friday 25 October and Monday 28 October 2013,
Vandals daubed paint on a nest swing, chains and handles of play equipment. They also tore up pieces of one of the playgrounds’ safety surfaces.
It is not known if the two incidents are connected.
PC David Minto, of Harrogate Safer Neighbourhood Team, said:
If you know anything about either of these acts of mindless vandalism I urge you to come forward straight away.
The damage has achieved nothing but causing inconvenience and unnecessary expenditure
Whoever is responsible should be deeply ashamed of themselves.
Anyone who can assist officers with this enquiry should contact Harrogate police on 101, select option 2 and ask for David Minto. Alternatively, information can be emailed to email@example.com
Or call Crimestoppers anonymously on 0800 555111, quoting reference number 12130187310.