Something like the following will work in SQL2000:
SELECT Z.statename, Z.CityName, Z.CountryName, COUNT(*) AS NumZips
INTO #t
FROM zip_xref Z
GROUP BY Z.statename, Z.CityName, Z.CountryName
UPDATE C
SET county = D.CountryName
FROM crime_table_08 C
JOIN
(
SELECT T.statename, T.CityName, MIN(T.CountryName) AS CountryName
FROM #t T
JOIN
(
SELECT T1.statename, T1.CityName, MAX(NumZips) AS NumZips
FROM #t T1
GROUP BY T1.statename, T1.CityName
) D1
ON T.statename = D1.statename
AND T.CityName = D1.CityName
AND T.NumZips = D1.NumZips
GROUP BY T.statename, T.CityName
) D
ON C.state = D.statename
AND C.city = D.CityName
DROP TABLE #t