Safety inspectors will handle inspection and safety controls on a crane site.
Overhead cranes, and gantry cranes require inspections to ensure they are safe to work around.
Earthquake requirements may have to be met as well as how a crane attached to that building affects it's preparedness for an Earthquake.
You should contact officials in either state or local government prior to installing or setting up a crane in order to see what regulations are required. Like many construction projects, documentation may be required to ensure you're operating within the law when it comes to overhead cranes.
Government-required inspections
Start with OSHA when it comes to certifying construction equipment.
OSHA creates and enforces standards for cranes, hoists and derricks.
Check the O.S.H.A website for information about where to find these regulations, and they are enforced by OSHA officers.
Local and state inspection requirements
In addition to OSHA, twenty five state governments will require the inspection of cranes according to OSHA-standards.Anytime a crane is used for construction or industrial purposes, the business operating that crane should check with state authorities to see what safety requirements exist.
Those who operate cranes without inspection or approval could face fines or orders to cease operations. An overhead crane may have different safety requirements from a large tower crane, and these requirements should be considered and reviewed before operation.
Finding a crane inspector
In many cases, a private company may be authorized to conduct crane safety checks and to certify a crane is safe.
This individual will usually work for the manufacturer of the crane or another private company authorized to conduct inspections.
Such a restriction only applies to very large cranes such as those used in construction and shipping. Cranes used in construction are often required to be inpected after servicing.
Other cranes not used in public areas, such as overhead cranes in manufacturing or industrial settings, may not be covered under the same rules, however, it's always possible that in your situation they might be and so you should check with local governing bodies to be sure.
A gantry crane, if resting on it's own gantry, may actually require inspections after maintenance is performed; and overhead cranes built upon a separate superstructure may also require inspections after maintenance.
There may also be a requirement that a crane be inspected by a crane engineer or technician on a regular basis, usually once a year, in order to remain in operation.
Inspection costs must be borne by the owner or operator of the crane.
Related resources:
Under Running Overhead Cranes
Wikipedia article on cranes
Information on Crane Safety