I recommend everyone watch this video. It's geared towards lawyers. If the police are asking questions with any level of suspicion at all, don't talk to them. Even if you do not lie, and are innocent, the things you say can still be used against you.
Summarizing:
1. There is no way it can help.
2. If your client is guilty (or even innocent), they might admit guilt with nothing in return.
3. If your client is innocent, they can still make some small mistake or tiny mistruth that can be used to convict by seeding doubt.
4. If your client is innocent, and does not make any small mistake or tiny mistruth, what is said can still be used in court to convict.
5. If your client is innocent, and tells the police absolutely nothing incriminating at all, the police can still mis-remember the conversation and result in a conviction.
6. If your client is innocent, and tells the police absolutely nothing incriminating at all, and the clients statements are videotaped so it cannot be mischaracterized, the police can still augment the conversation from their personal knowledge and result in a conviction.
There's more, it goes on and on and on. Don't talk to police if you are being questioned about something, whether you did it or not.
https://www.youtube.com/watch?v=d-7o9xYp7eE