LR-25 FLT CREW OVERSHOT ALT DURING AN APCH WHEN USING AN INCORRECT ALTIMETER SETTING THAT WAS PROVIDED BY THE ATIS AT LNK; NE.

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FLT PLAN -- ASE TO LNK. DSNDING INTO LNK; WE WERE SWITCHED TO ZMP FROM ZDV WITH A LEVELOFF AT FL240. ZMP CLRED US TO 11000 FT WITH AN ALTIMETER SETTING OF 30.45. THROUGH FL180; BOTH OF US SET THE ALTIMETER TO 30.45. I PICKED UP THE ATIS AND THE ATIS HAD THE ALTIMETER AT 30.44. AT 11000 FT; WE WERE SWITCHED TO LNK APCH AND I STATED WE ARE AT 11000 FT WITH ATIS INFO AND REQUESTED VECTORS FOR THE ILS RWY 35L APCH TO CHK OUR AUTOPLT ON THE APCH. WX WAS CLR AND VISIBILITY MORE THAN 20 MI. APCH GAVE US A DSCNT CLRNC TO 4000 FT AND A HDG OF 150 DEGS FOR VECTORS FOR ILS RWY 35L. LEVELING OFF AT 4000 FT; APCH INDICATED VFR TFC AT 12 TO 1 O'CLOCK POS AT 3500 FT WHICH I HAD IN SIGHT. A FEW SECONDS LATER; APCH CAME BACK AND TOLD US TO CLB BACK TO 4000 FT. I TOLD HIM THAT WE WERE AT 4100 FT. HE REPLIED 'I SHOW YOU AT 3600 FT.' HE THEN FOLLOWED WITH 'ALIMETER IS 30.04; DSND TO 3000 FT.' WE DIALED THE NEW ALTIMETER SETTING IN AND NOW OUR ALT MATCHED WHAT HE SHOWED ON RADAR. THE TFC WAS NO FACTOR AND HE CLRED US FOR THE APCH. WHILE TAXIING TO THE FBO; I LISTENED AGAIN TO ATIS AND IT BROADCASTED THE ALTIMETER SETTING AS 30.44. I MADE THE OTHER PLT LISTEN TO THE ATIS AND HE CONFIRMED THE ALTIMETER SETTING AS 30.44. I CONTACTED TWR AND TOLD THEM THAT ZMP HAD GIVEN US 30.45 AND THEIR ATIS HAD 30.44. SHORTLY AFTER THAT (LESS THEN 1 MIN); THE ATIS WAS PULLED OFF THE AIR. AFTER FUELING THE AIRPLANE; I LISTENED TO THE ATIS WHICH WAS NOW WITH THE CORRECT ALTIMETER OF 30 PT 04. WE LEFT LNK FOR HOME WITH NO FURTHER INCIDENTS.