Regulations do exist, but for a private single engine non-turbine airplane operated over water, no. You legally can fly without life preservers, raft, and most of the common-sense items that you should have. Regulations regarding life preservers, rafts, and survival equipment apply to aircraft operated for hire, and large and turbine aircraft, in the USA.
A better question with respect to single engine airplanes is whether you should be flying it over water in the first place, survival equipment not withstanding. Good airmanship in light singles involves keeping a viable landing site available at all times. Unless you have floats, water represents a multitude of hazards, especially in a fixed-gear airplane.
Even with survival gear on board, unless you're prepared to exit a sinking or sunken aircraft, while inverted and unable to see, and find the surface and then deploy your flotation gear, you probably shouldn't be over the water. A lot of private pilots do, on the notion that an engine failure, fire, etc, won't happen to them.
Worse, today we have the wealthier private pilot renting or flying the Cirrus, with it's built-in alternate airport: the parachute. A lot of pilots treat the parachute like an alternate airport. They tend to go places and do things they ought not, because they feel that the little handle is there to save them. Four occupants at night in a thunderstorm in the mountains deploying their parachute due to disorientation, is a good example. Flight overwater in a single-engine piston airplane is another, regardless of survival gear.
https://www.ecfr.gov/cgi-bin/text-id..._1205&rgn=div8
§91.205 Powered civil aircraft with standard category U.S. airworthiness certificates: Instrument and equipment requirements.
(12) If the aircraft is operated for hire over water and beyond power-off gliding distance from shore, approved flotation gear readily available to each occupant and, unless the aircraft is operating under part 121 of this subchapter, at least one pyrotechnic signaling device. As used in this section, “shore” means that area of the land adjacent to the water which is above the high water mark and excludes land areas which are intermittently under water.
For large (over 12,500 lbs) and turbine aircraft:
https://www.ecfr.gov/cgi-bin/text-id..._1509&rgn=div8
Subpart F—LARGE AND TURBINE-POWERED MULTIENGINE AIRPLANES AND FRACTIONAL OWNERSHIP PROGRAM AIRCRAFT
§91.509 Survival equipment for overwater operations.
(a) No person may take off an airplane for a flight over water more than 50 nautical miles from the nearest shore unless that airplane is equipped with a life preserver or an approved flotation means for each occupant of the airplane.
(b) Except as provided in paragraph (c) of this section, no person may take off an airplane for flight over water more than 30 minutes flying time or 100 nautical miles from the nearest shore, whichever is less, unless it has on board the following survival equipment:
(1) A life preserver, equipped with an approved survivor locator light, for each occupant of the airplane.
(2) Enough liferafts (each equipped with an approved survival locator light) of a rated capacity and buoyancy to accommodate the occupants of the airplane.
(3) At least one pyrotechnic signaling device for each liferaft.
(4) One self-buoyant, water-resistant, portable emergency radio signaling device that is capable of transmission on the appropriate emergency frequency or frequencies and not dependent upon the airplane power supply.
(5) A lifeline stored in accordance with §25.1411(g) of this chapter.
(c) A fractional ownership program manager under subpart K of this part may apply for a deviation from paragraphs (b)(2) through (5) of this section for a particular over water operation or the Administrator may amend the management specifications to require the carriage of all or any specific items of the equipment listed in paragraphs (b)(2) through (5) of this section.
(d) The required life rafts, life preservers, and signaling devices must be installed in conspicuously marked locations and easily accessible in the event of a ditching without appreciable time for preparatory procedures.
(e) A survival kit, appropriately equipped for the route to be flown, must be attached to each required life raft.
(f) As used in this section, the term shore means that area of the land adjacent to the water that is above the high water mark and excludes land areas that are intermittently under water.