I live in the United States. I believe that if an investor owns zero coupon tax free municipal bonds,the interest from their bonds must be reported on their tax return using the accrual method. Note that the interest from these bonds might be subject to state income tax. Is my belief correct?
Zero-coupon bonds that have a maturity date more than a year later are assumed to have earned interest anyway, and this imputed interest must be declared annually if the bond is held in a non-tax-advantaged portfolio. In a tax-advantaged portfolio (e.g. an IRA or a 401(k) plan), there is no such reporting requirement; the custodian can list the zero-coupon bond at its market value on December 31 for purposes of reporting the value of the account on December 31.
For zero-coupon municipal bonds, the interest is, of course, tax-exempt for Federal tax purposes(and nobody in their right mind will hold them in a tax-advantaged portfolio such as an IRA or 401(k) plan but YMMV). Once upon a time, interest income from municipal bonds did not even have to be listed on Form 1040 but nowadays, it is listed on Line 8b of Form 1040.
Series EE US Savings Bonds are zero-coupon bonds but are exempt from the imputed interest reporting requirement; the default is that interest is taxed when the bond is cashed in. However, it is sometimes better for children to declare the interest as it is earned each year and have it taxed at a low rate (might even be zero rate) than to have it all be taxed in the year when the bonds are cashed in to pay for college tuition etc.
See what FINRA has to say about zero-coupon bonds and the taxation of their interest.
Zero coupon bonds do not pay any interest, therefore there is no interest to report. They are sold at a deep discount, meaning you may much less that the face value. What they do report is the effective yield of the bond based on the discounted sale price. For example, you might pay $500 for a 10-year, zero-coupon bond advertised at a yield of 7.05%. So the first year you would accrue about $35 (7.05% * $500) in interest, and would accrue slightly more each following year since the yield is based on compounding interest.
This "interest", and interest from municipal bonds that do pay coupons might be subject to AMT and/or state taxes. That interest is generally reported on a 1099-INT as tax-exempt interest.