Is it necessary to have an employee handbook?

No, it is not totally necessary to have an employee handbook. Many companies do not have one.

Now, if you asked me if it is advisable to have one, my answer would be yes.

A good employee handbook conveys what kind of employer the company is -- what's important to top management and what kinds of behaviors are most desirable. A well-written handbook establishes clear "rules of the road" so that all employees can most easily understand the parameters of their department, their eligibility for company benefits, proper use of technology equipment, what kinds of behaviors may result in termination, how to resolve problems (think: harassment or other legal entanglements that might be avoided)

The list goes on and on regarding why having an employee handbook is a good idea. Your question is similar to, "Is it necessary to have laws in a civilizd society?" Again, no, it is not necessary -- but it is highly advisable.