Regardless of whether you work in government or not – for my money, the best book for a manager is Peter Scholtes’ book The Leader’s Handbook (also the Team Handbook). . . I’m also a fan of Stephen Covey’s 7 Habits for Highly Effective People, Brian Joiner’s 4th Generation Management, Tom Terez’s book 22 Keys to a Meaningful Workplace, Peter Block’s Flawless Consulting, Peggy Holman and Tom Devane’s The Change Handbook, David Chrislip’s The Collaborative Leadership Fieldbook, Alfie Kohn’s books, especially No Contest and Punished by Rewards, Peter Senge’s Fifth Discipline, Deborah Tannen’s work – including You Just Don’t Understand: Men and Women in Conversation or Talking 9 to 5, John Gottman and Joan DeClaire’s book The Relationship Cure, and GOAL/QPC’s variety of pocket book Memory Jogger series on tools and techniques associated with improvement and facilitation.
Somewhere every manager needs an introduction to statistics and control so they can insist on data-driven decision making and understand when variation is significant and signals a need for management investigation and intervention and when variation simply happens and they should not interfere in the underlying process that produces that variation. There are a variety of sources on that – but something by or about W. Edwards Deming should be on your list, as well as some kind of introduction to statistics and variation.