It is not enough to provide data—for people to be able to use it, they must understand the terms under which they are permitted to do so. If data is copyrighted, whether by government or a third party (e.g., a contractor), then copyright law prohibits them from reusing that data in most ways, and so your “open” data is not so open. It isn’t necessarily useless to publish copyrighted “open” data, but it’s close.
In some U.S. governments, this is a settled matter that requires no work on your part.
For example, all works created by the federal government are in the public domain, which is to say that federal data may not be copyrighted nor released under a particular license (with a few exceptions). People can do anything at all with such federal data, period. Some states function under the same legal standard, and permit neither themselves nor their subdivisions (i.e., cities, counties, towns) to claim copyright. Any data published by such governments should be explicitly labelled as being in the public domain.
Most states have practices that are more complicated, allowing copyright to be claimed under some or even many circumstances. When that is the case, you must determine for each dataset what its licensing status is, generally in consultation with the attorneys for the agency that produces that data.
To determine what copyright regime exists for your government, start by looking up your state in Harvard Library’s State Copyright Resource Center, which provides detailed information for what can and cannot be copyrighted in each state (and D.C. and Puerto Rico).
If you are in a position to do so, you should release data under a Creative Commons Zero (CC0) license, which waives copyright. This is arguably better than dedicating work to the public domain, because “public domain” is a concept that exists under U.S. law, but not internationally. CC0 allows anybody anywhere in the world to use your data, while public domain is basically limited to the U.S.
For more information, read Open Government Data’s “Best-Practices Language for Making Data ‘License-Free’.”