The IRS has several versions of the Notice CP01 but the most common is the CP01S (below):
Notice CP01S tells you the IRS has received your Form 14039 or similar statement claiming you've been a victim of identity theft. This notice is used when you initiate a claim of identity theft & is very similar in effect as Letter 5073C. Notice CP01 tells you that the IRS has verified your claim of identity theft. Notice CP01A notifies you that you've been assigned an Identity Protection Personal Identification Number. This number placed in the lower right hand corner of the 2nd page of subsequent tax returns you file - Form 1040.
Respond to Notice CP01
Many times, you discover you've been a victim of identity theft only when you get a big bill from the IRS or worse a threatening letter of impending levies (e.g., CP504). When you call them, you will be told there are 2 returns (or more) which have been filed. Sometimes it is simply an error by another taxpayer or the IRS. Other times a social security number is used for fraudulent purposes.
So, if you've truly been a victim follow the IRS advice, report it to your local police & inform your banks, credit card companies, etc. in case they want to change your accounts.
Various Types of IRS Notice CP01S: