A tale of two Sherlocks
Clearly, since copyright expires 70 years after the creator's death and Doyle passed away in 1930, Holmes has been out of copyright since 2000 which is why loads of people pile in and write books, make movies and TV series (an odd aside is that the UK's law used to say copyright stopped 50 years after someone's death, which is why Granada started on the Jeremy Brett series that year - only to find their character back in copyright when we harmonised with Europe).
So in principle there is nothing to stop CBS or anyone else making a Sherlock Holmes series. There is more, though.
CBS visited Hartswood to talk about an American series. Hartswood felt, perhaps understandably, that since there was already an American following for its "Sherlock" series starring Ben Cumberbatch, it didn't need to make another one.
Then this other idea crops up. Sue Vertue, producer for Hartswood, confirmed on her Twitter feed that the British company would be following the Americans' progress and look to copyright laws if necessary.
The tricky thing would no doubt be that "Sherlock" isn't the first modern-day Holmes. As long ago as the 1940s, Universal Studios placed Basil Rathbone and Nigel Bruce's Holmes and Watson into the Second World War, fighting a Moriarty who would be working for the Nazis. If CBS can demonstrate that Hartswood doesn't own a modern interpretation of Holmes and make theirs sufficiently different, there may be no case to answer.
That said, America doesn't always have a shining record when it comes to localising ideas that originated in Britain, even when rights aren't an issue. Anyone who has seen Roger Moore's Sherlock Holmes (I am not making this up, it was called "Sherlock Holmes in New York") is likely to agree.
There are successful transfers of course. "The Office" has survived longer than the UK template and even got through a change of lead character. Others have been less so; various attempts have been made at an American "Fawlty Towers", including one in which Basil Fawlty was dropped as unnecessary; the American "Life On Mars" bombed and the less said about "Red Dwarf" as a Stateside show the better.