Answer
No, it is not necessary for the charged body to actually touch the ball of an electroscope.
Work Step by Step
You may want to refer to Figure 22.13. If, say, a positively charged object is brought near the ball, some electrons from the leaves are attracted up into the ball, leaving the gold leaves with a net positive charge. The leaves will spread apart. A similar argument explains why the leaves will spread apart when a negatively charged object is brought near the ball.
This is an example of charge separation due to induction.
