Ok, I've got a better idea.... don't phone and ask because they will just think your weird, or tell you that you can't do this. Of course - city or state parks do not want people planting random flowers, especially if it is a park that still has its ecosystem somewhat intact. the company I work for deals with restoring parks by getting rid of the invasive species of plants that are taking over, mostly as a result of these plants spreading from nearby gardens.
A better way to go about it is to plant native species and drought-resistant wildflowers in areas of your town that are neglected or abandoned. This is called guerilla gardening and its one of the fastest growing urban renewal movements. This way, your spreading nature through your city into the places that need it the most, and your not encroaching on land that is already set up as park space.
Guerrilla gardening is wholesome mischief. It breaks the law but improves public property. Because its wholesomeness is clearly apparent, some cities have started to institutionalize guerrilla gardening, with programs that invite local residents to “adopt” and plant traffic circles, boulevards, and other pieces of public property.
GuerrillaGardening.org
Guerrilla Gardening Links
The Urban Planter
You Grow Girl™ - Gardening for the People
Okay, I hope that was of some help for you..... take a look around your neighborhood and see if you can find any land that is not being used, that could be turned into a garden .......