Switzerland doesn't have one national leash law the way Italy does. Dog leash and muzzle rules are set canton by canton — Switzerland has 26 of them — and sometimes further refined at the municipal level, so the same walk can have different rules a few kilometres apart. The one constant is federal: owners must always control their dog well enough that it doesn't endanger or seriously bother anyone.
The rule that applies almost everywhere, regardless of canton, is a seasonal one: dogs must be leashed in and around forests during the wildlife breeding season, typically 1 April to 31 July, to protect nesting birds and young animals. Exact dates and the leash zone's width vary by canton, so check local signage — it's usually posted clearly at trailheads.
A handful of cantons — including Zurich and Fribourg — also restrict or ban certain breeds classified as potentially dangerous, sometimes requiring a permit, a training course, or a muzzle in public for listed breeds. If you're travelling with a breed that shows up on any of these lists, check the specific canton you're visiting before you go, since the rules genuinely aren't the same country-wide.