How should a company screen applicants for Customer Service Representative?

First step should be by a phone interview, it's very important to check the applicant voice tuning and way of speaking.

Secondly, a face to face interview, so you can check the applicant body language and face expression.

Finally,a friendly talking with indirect questions will show the ability of solving problems and handling complains.

You need to see if the person is able to speak well. You can find this out by conducting an unexpected phone interview. Notice if the person is able to converse with you and not just giving you plain yes and no answers.

Look for friendliness in their tone. 

More than often, people make a mistake of hiring someone with more experience than a delightful personality for customer service, which I believe can be harmful for the company in the long run.