Under the SIS, which the UK joined in 2015, police and border forces in EU member states and four “associated countries” enter and receive alerts about wanted and missing people, as well as potential witnesses and items that could be used as evidence.
Both the UK and EU backed close cooperation on security matters when they outlined their Brexit negotiating strategies.
In the document setting out its negotiation aims, the government lists the SIS as an example of the “mutually beneficial model of cooperation” in the fight against crime and terrorism.
It said the UK would “continue to cooperate closely with our European partners” on security matters, and “negotiate the best deal we can with the EU to cooperate in the fight against crime and terrorism”.
But Mr Clegg said the UK would be “severing our ties” with the system by refusing to accept rulings of the European Court of Justice after Brexit.
“It is hard to overstate the importance of this database,” said Mr Clegg, the former deputy prime minister.
“We check it 16 times a second, looking for security threats that have been flagged to us by other European countries. And we use it to tell other countries to stop and question people who we think are potential terrorists.”
He added: “If she fails to back down, Theresa May’s approach to Brexit poses a direct threat to our national security,” he said.
The SIS is in use across the borderless Schengen area, with special arrangements for countries – like the UK – that are not part of the passport-free zone.
A Conservative spokesman said: “The Lib Dems are peddling nonsense – we’ve made clear that under Theresa May security cooperation will be an important priority in the negotiations, and it’s not in the EU’s interest to lessen that relationship.”