Use of a book for a continuing education course
Yes, you can require your students to read a book for a class. Where the students get the book is then their problem, and as long as you don't provide them with pirated copies, the origin of their copies needs not be your concern.

The only concern many of us have these days is that many books are expensive. This may not be true for a softcover copy of some classical literature, if that happens to be your area of teaching, but it is an issue if your area is some advanced topic in the sciences where many textbooks can run at $100 or over. I have generally avoided requiring my students to have a particular textbook for these reasons -- going to college is expensive enough these days.