These expenses would be considered an out-of-pocket charitable cash contribution.  You will want to ensure you have documentation to support this deduction.

Would a sheriff's office be considered a charitable organization?

Yes.  The following is an excerpt from the IRS Publication 526:

Types of Qualified Organizations:
5.  The United States or any state, the District of Columbia, a U.S. possession (including Puerto Rico), a political subdivision of a state or U.S. possession, or an Indian tribal government or any of its subdivisions that perform substantial government functions. (Your contribution to this type of organization is deductible only if it is to be used solely for public purposes.)
Example 1. You contribute cash to your city's police department to be used as a reward for information about a crime. The city police department is a qualified organization, and your contribution is for a public purpose. You can deduct your contribution.

Example 2. You make a voluntary contribution to the social security trust fund, not earmarked for a specific account. Because the trust fund is part of the U.S. government, you contributed to a qualified organization. You can deduct your contribution.