Q: If I modify a Japan art work that is copyrighted am I subject to American or Japanese Copyright law?

A: In this case, there are a few key considerations:

1. Jurisdiction: Generally, copyright infringement lawsuits are governed by the laws of the country where the lawsuit is filed. As you're based in the U.S., it's likely that U.S. copyright law would apply if a lawsuit was brought against you in the United States, even if the original work is Japanese.

2. International Treaties: However, the U.S. and Japan are both signatories to the Berne Convention and other international copyright treaties. These treaties provide certain minimum protections and reciprocity between member countries.

3. Fair Use (U.S.) / Fair Dealing (Japan): Both the U.S. and Japan have provisions in their copyright laws that allow for certain uses of copyrighted material without permission, such as for purposes of commentary, criticism, news reporting, teaching, scholarship, or research. In the U.S., this is known as "fair use," while in Japan it's referred to as "fair dealing." Whether your use qualifies would depend on a number of factors.

4. Non-Profit Status: The fact that your use is non-profit and you don't intend to sell the image could weigh in favor of fair use under U.S. law. However, non-profit status alone does not automatically qualify a use as fair.

5. Extent of Modification: The degree to which you've transformed the original work is also a key factor. The more transformative your use is, the more likely it is to be considered fair use.

In summary, while Japanese law could theoretically apply, U.S. law is more likely to govern if a suit was brought against you in the U.S. Your non-profit status and the extent of modification to the original work would be important factors in determining whether your use is permissible under U.S. fair use doctrine. However, predicting the outcome of a fair use argument is notoriously difficult. If you're concerned, the safest course is always to seek permission from the copyright holder.