It depends on where you are. Are you in a public library or a public funded university? In the latter case are you considered faculty or merely employees of the university? Excluding faculty, then yes, you are a civil servant employed in civil service. All hired, non-appointed, non-extraordinary (not hired for credentials, political appointment, or academic expertise) public employees are civil servants. But not all librarians are civil servants. So, special librarians, tenured, private archivists, endowed museums, whatever.

This civil service/customer service dichotomy is one of my pet peeves. In many ways, people form opinions about "the government" via their interactions with low level civil servants like the police, us, the fire department, and weird government/not government agencies like amtrak and the Post Office. When you've got some asshole going "la-di-da, lady, I'm a civil servant, I don't do customer service, so I'll get to you after my break and once I finish stamping" that's something that's going to bite you, as an organization, in the ass come election time, or at the next board meeting. That employee is a toxic employee who is doing real harm to your work culture. Ever go into the Post Office and see that dude just sitting behind the rest, talking about his lunch real loud or his grandmother's cooking or shouting back into the warehouse about how Lonnie can't handle a forklift, while a line of 20 people slowly wends it's way through one cashier? That's what people think about rightly or wrongly when they think of Civil Service/Civil Servants: overpaid underachievers doing the minimum to keep their jobs and keep things moving. You want to stay the hell away from that impression. Shit, if I heard that kind of flippant bullshit -- and that's what it is, bullshit -- coming from an employee's mouth, they'd be in a month's worth of customer service classes with a referral letter to the personnel board on a second offense.

That's unacceptable. There's no "civil service" model of service. That's the category of employment we work in. It's all customer service 24/7, all the way up and all the way down. If one doesn't understand that customer service is the only goal of any organization civil, governmental, private, corporate, ngo, whatever, they need first STFU and second read a book about it. Damn.