Rzasawa was formerly part of the German Empire. In the German Empire, the place was called Rząsawa.
The place is now called Rząsawa and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Rzasawa | Russian Empire | Petrokov | 1914 |
| Rząsawa | Poland | Piotrków | 1921 |
| Rząsawa | German Empire | Lask | 1939 |
| Rząsawa | Poland | Bełchatów | 1945 |
| Rząsawa | Poland | Piotrków | 1992 |