Your comment/question about why would someone investigate your theft is immature at best, at that is being very kind to you.
Now your question. A civil demand letter need not be paid since it does not create an independent obligation to pay. You must pay attention to any contact by police authorities or any contact from the courts.
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There's no real investigation to do be done. You like signed some kind of admission with asset protection, so it's basically up to them whether they will call the police or not. Why wouldn't they? Do you realize how much wal-mart would lose if there were no repercussions when people attempted to steal merchandise?
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If you weren't arrested, or charged with an offense or given a court date then you aren't being prosecuted. You will probably receive a civil demand letter asking you to pay. I generally advise clients to disregard these demand letters. You don't owe them anything. In order for you to actually owe them something they would have to sue you and win. The cost of doing so (even if they could win) is substantially greater than any amount of money they could possibly recover and as such they don't pursue it. They send out these letters hoping hat you do t know better and simply send them the money. Nothing will happen to you if you dont pay it. If on the other hand you receive something from the police or the courts don't ignore that and contact an attorney ASAP for assistance.