These civil demands are made all over the country. What they are demanding is usually the maximum a court could grant as a civil penalty if the store sued you (this would be in addition to the value of the item stolen and any court costs and any attorney's fees awarded), which in Colorado is $250. These demand letters are almost always from a firm hired by the major department stores to send out these letters, and it is usually just in the hopes people will simply pay rather than risk a lawsuit. I haven't seen one for less than the maximum, so I don't know why your's is different.
There are many reasons attorneys cite for not paying this fee including the fact they are seeking the maximum penalty they could get as well as concerns over its effect on pending criminal charges for the theft. Further, I have never heard of anyone being sued after ignoring these demands, and some attorneys claim no lawsuits have ever been filed by at least one California firm that sends these letters. The practical consideration is how much money is involved; if it were thousands of dollars I could see a store pursuing a lawsuit, but for a more typical theft amount plus a possible civil penalty, it seems unlikely.
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Anyone can make demands for you to pay. You can either pay up and not be bothered by it or you can put their feet to the fire and make them try to get a court to order you to pay the amount. There is always a risk of being sued in civil court. However, like everything else in else you calculate the risk of the suit being actually filed and the court actually ordering the amount demanded. If your daughter is innocent then she should fight the criminal case and not take a guilty plea which will be on her juvenile record for some time. But theft is a crime of dishonesty and can haunt her for a very long time. Civilly, you can wait and see of they actually sue her or you for the amount. Such suits are a rarity since the amount demanded is so small.