Homeowners are generally allowed and encouraged to plant street trees, which are trees planted in the strip between sidewalk and curb. However, such plantings must be in compliance with Zionsville town regulations. These are available here.
The ordinance includes a list of recommended tree species and also prohibited tree species. Please note that Zionsville requires a permit for planting street trees, but it is a simple matter to obtain this permit. You should know what you are planning to plant, have your utilities marked (call 8-1-1 for this free service), choose the locations for your trees and then apply for the permit. The Town will need to confirm that your planting location is not too close to utility or drainage lines. Please note that the utility marking service will not detect your sprinkler system. Any sprinkler lines that will be affected by tree planting are the homeowner's responsibility. After the trees have been planted, they are technically the property of the town, since Zionsville owns the curb strip land. This means that if a tree dies after the warranty has expired, you can request that the town replace it. However, this will undoubtedly be a low priority for the town, and it may take them years to get to it.