More than 500 cases have been heard in Scottish courts as a result of the European arrest warrant (EAW), Crown Office figures show.
The European Union (EU) justice measure has also seen 367 people extradited from Scotland to face courts in Europe, according to figures obtained by the Scottish Parliament Information Centre (Spice).
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The SNP say these cases may not have been possible without the co-operation of fellow EU member states and urged Prime Minister Theresa May to maintain cross-border co-operation on justice following the Brexit vote.
SNP MSP Ben Macpherson, a member of the Scottish Parliament's Justice Committee, said: "The EAW is a perfect example of how working together with our friends and allies in Europe helps keep us safer - and that this has been put at risk thanks to the irresponsible actions of the Tory government is simply unacceptable."
He said the 541 cases heard in courts in Scotland as a result of the EAW "might not have been possible without the co-operation and support of other European nations".
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"That this is being put at risk demonstrates the absolute folly of Scotland possibly being dragged out of Europe against our will," he said.
"Nicola Sturgeon has been clear that she is exploring all options to keep Scotland's place in the EU - including independence if that's what it takes - and, in the meantime, Theresa May must confirm that she will do everything she can to ensure that this vital cross-border co-operation on law and order continues."
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