As an initial matter, it is important to note that the federal Freedom of Information Act (FOIA) does not apply to state public records. If you want a police report from your local police department, do not invoke FOIA. They may give you the report anyway (because the state public records law says they should), but they may deny your request because you cited the wrong statute.
While Arizona's public records law generally gives the public access to any public record, it allows certain information to be withheld or redacted to protect those vulnerable to attack. Identification and contact information for a crime victim cannot be disclosed. The home address and home telephone number of certain individuals involved in law enforcement (which can include not just police officers, but also prosecutors, and people who work in this area) is confidential. Photographs of police officers may only be released in certain circumstances. Federal risk assessments of infrastructure (such as telecommunications or utilities) are exempt from disclosure.
Information may be withheld for certain important purposes. For example, the location of an important archaeological find may be withheld to protect the site from vandalism or damage. If the custodian of a record believes that a record that is requested for commercial purposes (such as to compile a mailing list for business solicitations) will be abused, the custodian may seek an order from the governor preventing the record from being released. Adoption, severance, and dependency records held by the juvenile court are exempt.
Some information that is considered private and confidential is exempt from disclosure. For example, some information contained in a public employee's personnel file, such as Social Security numbers and medical information, is protected (but not completely prohibited) from disclosure by federal law. Disciplinary actions, however, are not confidential, and are required to be disclosed.
Finally, Arizona courts have found that certain records may be withheld if the agency believes that "the interests of privacy, confidentiality, or the best interest of the state in carrying out its legitimate activities outweigh the general policy of open access." This exception is usually invoked to protect the details of an ongoing police investigation, the identity of a confidential informant, or some other particularly sensitive information. It is not meant to be a catch-all, however, nor does it give the agency discretion to pick and choose what information it wants to release. The agency must be able to justify its withholding of information under this exception. If you don't get the police report you ask for, though, this is probably the reason.