You should never consent to requests by the police to search you, your home or your car. In most cases, if the police confront you or ask to search you (or your home or car), then this means that they already suspect your involvement in something illegal. So there is likely nothing you will be able to say that can change their minds from wanting to investigate you. Police officers are trained in interrogation tactics and will not ease up on questioning and pestering you if they think you have any involvement. The surefire way to stop a conversation with an officer is to tell them that you wish to remain silent and that you would like a lawyer. If a police officer already wants to arrest or search you, they will always be able to find a legal way to do it. However, just by talking to them, you are playing into their hands and doing exactly what they want, regardless of if you are truly innocent or not. If police do not legally search your car, home, or your body, the evidence will not be permissible. But, if they search you illegally and you consented to the search, evidence will be permissible. So just saying no to a search is always the best bet.
Even if you are truly innocent of the crime they suspect you of, telling a small lie will hurt you in the long run. Think about it this way: you have no involvement with the crime, but the police know a certain individual is involved and think that you helped him or her. You have a solid alibi because you were with your friends the night that the crime took place. However, during questioning, you state that you were with friends, and you never even met the other suspect (when you know them). If police uncover evidence that shows that you know the other suspect, your credibility will be in a lot of trouble. The police will disregard anything you say to prove your innocence, and if your case ever goes to a jury, they will most likely do the same. It is not worth the risk of telling a small lie. Police officers are legally allowed to lie to you in order to siphon information that can lead to a break in the case. They may tell you that they have video of you committing the burglary and or that they have found a piece of your hair at the crime scene. Although none of this may be true, it can cause you to admit to something that will be held against you. If police try to play good cop and explain that if you cooperate they can cut you a deal in the process, do not fall for it. In some states like Maryland, police do not have the authority to cut a deal with you and the power rests in the hands of the prosecutor. So if you are approached by an officer, remember, do not talk! Speak with an experienced attorney.