Going by the wiki it looks like the calendar setup has been inconsistent between games, but the last few have more or less lined up with the real world as far as length of month and number of months. So, leap year or no? Has anyone checked?
Why should there be a leap year? Nirn is no planet like earth. From what I know about the lore, the Mundus (with Nirn and its moons Masser and Secunda) is surrounded by the void of Oblivion. The stars are holes in Oblivion torn by the Magna Ge through which Aetherius shines through. The biggest among them is the sun, the hole that Magnus himself made.
Now of course it is possible that the realm of Oblivion and Aetherius are more than three-dimensional, so a hole in 2D would be a sphere in 3D, in which case Nirn could indeed go around the sun at a speed that doesn't align with its day-and-night cycle (making a leap year necessary), but why would that be the case? There is no reason for Nirn to go in circles around a 3D hole. It's not even certain that on Nirn the seasons, which the months are clearly named after, are being caused by the sun/axial tilt like on earth.
Tl;dr: The creators of the lore just made it similar to our calendar. There is no need for leap years which is why I doubt that there are.
This Bosmer was tortured to death. There is nothing left to be done.
That said, Tamriel basically uses the Gregorian calendar for no actual in-game reason (e.g. why is Sun's Dawn shorter than all the others? Because February is, nothing to do with Tamriel.) So when matching in-game dates to real dates, it implicitly assumes leap days in order for everything to match. In 2016 (a leap year), you'd match 28 Sun's Dawn with Feb. 28 but 1 First Seed with March 1, and insert an inofficial, inexistent leap day for convenience reasons.
In the end, esp. since TES3:Morrowind, the Tamrielic calendar is all about convenient matching to the Gregorian, from its months to its seven-days-week to its names for days of the week (Turdas is called that because of English Thursday, no in-game reason).