The general consensus among scientists is the minimum safe distance for a supernova is in the range of 50-100 light years as noted here - http://earthsky.org/space/supernove-distance.
It really depends on what kind of supernova explosion takes place. In general, supernovae release huge amounts of x-rays and gamma rays, and these could significantly damage the ozone layer in the atmosphere when they reach the Earth. A depletion of the ozone layer could have catastrophic effects for the biosphere, as primary producers would significantly be affected after exposure UV radiation from the Sun, which could lead to a collapse in food webs globally.
I'm not 100% sure, but IMO the radiation should affect human satellites near Earth as well.
Chronos, PWiz, and rootone have all claimed that a supernova at the distance of 4.3 light-years would be catastrophic for life on Earth. I'd like to examine how you came to this conclusion. I discount the link Chronos posted, since it is full of obvious errors. First, it confuses years and light-years, an elementary mistake. Second, it states that, if the sun were to go supernova, the side of the Earth facing the sun would be boiled away. This is silly; since supernova explosions last for weeks, all of the Earth's surface would be impacted. Third, it states that, "The sudden decrease in the sun’s mass might free the planet to wander off into space." This is also nonsense. So ignore that article. What are the facts? A typical supernova has an absolute magnitude of about -18, and this luminosity lasts for a few weeks. At a distance of 4.3 light years, this would be an apparent magnitude of about -27.5, as compared to the sun at -26.7. So the Earth would have a second sun for a couple of weeks. This would clearly wreak havoc with the weather, but it wouldn't be a sterilizing event, and I think we would clearly survive. As far as X-ray and Gamma-ray emission, the articles I could find indicate that these emissions are far less than the emission of visible light. We are not talking a gamma ray burst, which would clearly be catastrophic at this distance if it were pointed at us, but an ordinary supernova. Gamma ray bursts are very rare events, and the odds of one happening nearby are extremely small. All of this is a long-winded way of asking whether anyone can back up the statement that a supernova 4.3 light-years away would be a sterilizing event.The blast from a supernova can be somewhat directional, so the exact consequences for Earth could vary because of that,
However even if Earth were located well away from the regions of maximum blast, I'm pretty sure that the amount of gamma radiation received from a supernova that close to Earth would likely sterilize all life, and probably fry the atmosphere into a highly ionized state.