There are lots of twists and turns to the story, and the timeline is not entirely clear to me, but the story apparently begins in Germany during the early 1990s. The American Central Intelligence Agency (CIA) manages to get their hands on a vast collection of files purporting to contain information on people who were employed by or somehow connected to the Hauptverwaltung Aufklärung (HVA), the foreign intelligence agency of the East German Ministry of State Security, Stasi. The files, known as the Rosenholz files, contain some 350,000 documents.
The Rosenholz files would remain in American hands until 2003, when all files were turned over to Germany. (Die Welt, German Wikipedia)

At some point during the early 1990s, the CIA apparently shares information on Stasi with SuPo. This information, which has become known as the Tiitinen list (named for Seppo Tiitinen, who was head of SuPo at the time), allegedly contains the names of about 20 Finnish citizens considered by Stasi to be "key contacts". The people named on the list remain unknown to the public, as then president Mauno Koivisto orders the list to be sealed. Speculation as to who exactly is named on the list runs rampant. Whether the information contained on the list emanates from the Rosenholz files is unclear.

In 2000, the United States offers to share parts of the Rosenholz files with the Finnish government, who accept the proposal. The government decides that the material should be made available to Finnish researchers, but this never occurs. The SuPo maintains the Rosenholz files contain the same data as the information they received earlier in the 90s, and refuses to grant anyone access to the Rosenholz files. Things take an interesting turn in 2007 when Finnish newspaper Aamulehti contacts the SuPo, who denies the files exist altogether! (Hufvudstadsbladet)
After Aamulehti requests comments from all government ministers, Prime Minister Matti Vanhanen essentially "orders" his cabinet to not answer questions in the matter, a course of action which in itself becomes a minor controversy. (Hufvudstadsbladet)
The Finnish political class seem divided on the whole affair, with some politicians coming out in favour of making the material public, and some politicians coming out in favour of keeping the material secret.
The statements regarding what material SuPo actually possess has become ever more conflicting, ranging from SuPo having files relating to Stasi though not from the Rosenholz files, to SuPo having knowledge of what the Rosenholz files contains though not possessing the actual files themselves, to SuPo being in possession of the Rosenholz files and them being merely a small part of SuPo's Stasi archives. (Hufvudstadsbladet)

The value of the information contained in the Rosenholz files seems to be highly questionable, as the vast majority of the people named in the files had little, if anything, to do with Stasi, and a person being named in the files thus could not be considered proof of interaction or collaboration with Stasi. (Hufvudstadsbladet, offline article, July 27, 2007)
Which brings us to a man named Alpo Rusi. Rusi is currently an ambassador and was former president Martti Ahtisaari's right hand man and a candidate in the Finnish parliamentary elections of 2003. In September 2002, Finnish broadcasters Yle breaks the story that SuPo is investigating Rusi for supposed connections to Stasi. Rusi denies the allegations, but decides not to stand for election in 2003. As it turns out, the investigation of Susi began during the spring of 2002. Rusi was informed of the investigation and instructed not to discuss the investigation with anyone. Someone at SuPo did however leak information, as politicians and even friends of Rusi's became aware of the investigation before Yle finally breaks the story.
In October 2002, Rusi's brother Jukka confesses to having cooperated with Stasi, but investigations continue, with SuPo leaking information to the effect that Rusi engaged in espionage. However, in June 2003, the prosecutor announces that no charges will be filed. Rusi has since attempted to get the files on his investigation made public in order to completely clear his name. He also maintains that the accusations derailed his political and professional career, and has sued the Finnish government for damages. It would appear the information that prompted the SuPo to begin the investigation in the first place was contained in the Rosenholz files. Which they have claimed they're not in possession of. (Hufvudstadsbladet)

There are many questions that remain unanswered, but they can essentially be summed up as: what did the SuPo know, and when did they know it? The picture that emerges of the SuPo from this whole story is not particularly flattering; an apparent historical artifact from a time in history when Finnish society was not as open as it is now.