@Jeruba Cops might just want you to give a statement as a witness or they may have you in mind as a potential suspect. There have been cases where people were arrested and convicted of killing their spouses. In pretty much every case the spouse that ended up getting charged was willing to talk to the police without an attorney because they knew they had done nothing wrong. But police often look at a spouse or a relation as the primary suspect. So they are starting and ending their investigation with proving that person is guilty. If it is something serious, you might want to get an attorney with you when you are questioned, even if you had nothing to do with the crime.
As for telling them you don’t want to talk or that you want an attorney, you always have that right. Always. And you can simply tell them that you aren’t comfortable talking with them without an attorney. It is that simple. Once you say that, they cannot continue to question you until you have an attorney present.
Of course, if you don’t know anything about whatever they are asking you can always tell them that. If you were out of town when your neighbor was burgled, you can simply tell them you were out of town and just heard about it.