Is it legal to arrest a seventeen year old girl with no prior record and put her in the prison for writing on public property?

My 17 year old daughter was arrested August 12, 2012 for writing the words "if we were only" on a park table. She wasn't read her rights and was put in a cell overnight until Monday when she was transferred to another site. My daughter has no prior records. She was held over night and called a criminal. Some of the police officers said this is what happens when we have too much time in our hands. Other neighborhood officers that know my child from the community areas said this arrest was ridiculous, these are good kids, as the community youth sergeant yelled,"This should teach you a lesson not to write on private property". Is this legal to hold a 17 year old female over night and hold her in a criminal cell for writing four words measuring less than 5 inches on a park table?