The clear-up rate for tracing offenders was also more than twice the rate in England and Wales so far in 2019-20.
The latest figures, for April to August, came at the first meeting of a new committee to scrutinise rail policing in Scotland after ministers shelved plans to merge BTP with Police Scotland.
BTP Assistant Chief Constable Charlie Doyle told the Scottish Railways Policing Committee: “Crime is down in Scotland which is contrary to the England and Wales position.
“Assaults against rail staff were down 20 per cent.
“It is a positive start to policing the railways in Scotland in 2019.”
Total reported crimes fell by 2 per cent to 747, while “violence without injury” offences were down by 4 per cent.
However, “serious violence” offences increased from nine to 14. Football-related crime also increased, from 25 to 32 offences, with hotspots at Haymarket in Edinburgh and Perth, involving fans returning from matches in the west and north.
No figures were produced for the increase in England and Wales crime since April, but crime across BTP increased by 12 per cent in the year to March compared with 2017-18 while it fell by 6 per cent in Scotland.
The overall clear-up rate in Scotland since April was 39 per cent compared with just 15 per cent south of the Border.
The rate for “violence against the person” offences was nearly 60 per cent, and sexual offences almost 66 per cent – both far higher than in the south. There was a 72 per cent clear-up rate for football-related crime.
Chief Superintendent Eddie Wylie, BTP’s divisional commander for Scotland, put the falling crime rate down to close working with Police Scotland “to ensure BTP doesn’t work in any type of silo”.
He also praised the “excellent levels of investment by Abellio ScotRail in CCTV”.
The force is trialling technology enabling CCTV footage to be shared across the country “at the press of a button”.
Mr Wylie also said BTP, as a Britain-wide force, could track potential crime “end to end”, such as oil rig workers drinking on trains from Aberdeen, which led to anti-social behaviour in places such as Newcastle and Sunderland.
He said BTP had also focused on six “key strategic locations” in Scotland where crime harmed the network most.
This had resulted in an 80 per cent reduction in train delays, including over 90 per cent at Bellgrove in the east end of Glasgow, on the Glasgow-Edinburgh line via Bathgate.
A ScotRail spokesperson said: “Recent figures show that reported crimes in Scotland fell over the past year, and crime on Scotland’s Railway remains lower than anywhere else in the UK.
“We will continue to work closely with the British Transport Police to clamp down on unacceptable behaviour and prosecute offenders.”