As Fisherman 13 said, no you don't have to catch and keep. There is not a law on the books in reference to trout that says you do. Some places will state that you do until you push the issue and know the law and it quickly becomes a suggestion. Some individuals will say that you do also, most of the time it will be individuals that are not catching fish or bait fisherman. You can choose to handle that the way you want to, but they are wrong. Some State park employee's will also say you have to keep what you catch, that to is wrong. Ask to talk to a Game Warden or call one yourself. As Fisherman 13 also said, to help keep the peace if your not keeping fish give them away.
This question comes up every year!
Micah 6:8 He has shown you, O mortal, what is good. And what does the Lord require of you?
To act justly and to love mercy and to walk humbly with your God