Connecticut property owners have an obligation to keep you and the rest of the citizens of the state safe from preventable injuries. However, what constitutes dangerous property conditions or poor maintenance might be subject to some discussion.
As defined by FindLaw, the personal injury law system in the state is based on negligent parties paying injured parties. While the behavior that actually counts as negligence is likely to vary from one case to another, there are some common events and conditions that could lead to a court deciding that a slip-and-fall accident was the property owner's fault, at least to some degree.
One common example of unsafe conditions in New England and other temperate climates is inadequate ice and snow removal. Whether it is the responsibility of a business owner, a property manager or a neighborhood association, is likely that somebody or some type of business entity should be keeping the sidewalks and walkways clear of slippery winter ice.
Of course, falls on slippery floors are not constrained to the winter season. For example, inadequate lighting or malfunctioning cooling equipment in a grocery store freezer aisle might lead to wet conditions on slick tile floors. Similarly, lack of repair of air conditioning equipment in a shopping mall might cause leaks to pool water under vents or ductwork, causing hazardous conditions.
The bottom line is that you should be safe to walk around public areas and open places of business. If the negligent action of the property owner leads to dangerous property conditions, and the owners or mysteries make no effort to remedy the situation or notify you of the danger, then their actions could constitute negligence under Connecticut law and entitle you to compensation for the losses caused by your injuries. Please do not use this as legal advice for any real situation. It is only meant as background information.