Some cleaning products and air fresheners, even so-called “greener” ones, though they may not contain any Formaldehyde directly, may produce Formaldehyde if they contain Terpenes – “the main constituent of essential oils derived from oranges, lemons, other citrus, lavender, thyme, cedar wood, pine, and other plants, flowers, and trees” per scientific sources - that react with ozone from air pollution to produce VOCs such as Formaldehyde.

According to Lawrence Berkeley National Laboratory:
“The use of cleaning products and air fresheners indoors can cause inhalation exposure of cleaning personnel and building occupants to toxic air contaminants (TACs). In addition to direct inhalation of toxic constituents of the product, many products contain terpene hydrocarbons and terpenoids that can react rapidly with ozone, yielding secondary pollutants. Ozone is commonly present indoors owing to infiltration of outdoor air and ventilation. Indoor sources of ozone also exist, including some photocopy machines…The products of ozone reactions with terpenes and terpenoids include volatile carbonyls, some of which are TACs (e.g., formaldehyde and acetaldehdye)…” http://energy.lbl.gov/ie/pdf/LBNL-57038.pdf

In June 2013, the U.S. Department of Health and Human Services added eight substances to its Report on Carcinogens, a science-based document that identifies chemicals and biological agents that may put people at increased risk for cancer. One of them is Formaldehyde.

The release also stated:
"A listing in the Report on Carcinogens does not by itself mean that a substance will cause cancer. Many factors, including the amount and duration of exposure, and an individual’s susceptibility to a substance, affect whether a person will develop cancer."

Still, prudent avoidance makes sense.

According to Dr. David Mudarri, former Senior Scientist with EPA:  “A professionally managed cleaning program is an important feature of a healthy facility. Improper cleaning products and processes can be major sources of pollution, whereas skillfully directed cleaning activities are a major factor in preventing or removing pollutants. Thus, it is vitally important to recognize that even so-called ‘greener’ products should be evaluated for their impacts as used.”

What to Do:
Ask your supplier if your cleaning products contain Terpenes
If they do, replace them with more benign formulations
Always ensure adequate ventilation when using any cleaning products, even natural ones.