Here is the data I found:
County Population Method
adams 28,026 Punch Card
allen 108,241 Op-Scan
ashland 53,749 Op-Scan
ashtabula 103,120 Punch Card
athens 64,380 Punch Card
auglaize 46,740 E-Vote
belmont 69,636 Punch Card
brown 43,807 Punch Card
butler 343,207 Punch Card
carroll 29,599 Punch Card
champaign 39,544 Punch Card
clark 143,351 Punch Card
clermont 185,799 Op-Scan
clinton 41,756 Punch Card
columbiana 111,523 Punch Card
coshocton 37,132 Op-Scan
crawford 46,091 Punch Card
cuyahoga 1,363,888 Punch Card
darke 52,960 Punch Card
defiance 39,054 Punch Card
delaware 132,797 Punch Card
erie 78,709 Op-Scan
fairfield 132,549 Punch Card
fayette 28,158 Punch Card
franklin 1,088,944 E-Vote
fulton 42,446 Punch Card
gallia 31,398 Punch Card
geauga 93,941 Op-Scan
greene 151,257 Punch Card
guernsey 41,362 Punch Card
hamilton 823,472 Punch Card
hancock 73,133 Op-Scan
hardin 31,608 Op-Scan
harrison 15,967 Punch Card
henry 29,318 Punch Card
highland 41,963 Punch Card
hocking 28,644 Punch Card
holmes 40,681 Punch Card
huron 60,231 Punch Card
jackson 33,074 Punch Card
jefferson 71,888 Punch Card
knox 56,930 E-Vote
lake 228,878 E-Vote
lawrence 62,550 Punch Card
licking 150,634 Punch Card
logan 46,411 Punch Card
lorain 291,164 Punch Card
lucas 454,216 Op-Scan
madison 40,624 Punch Card
mahoning 251,660 E-Vote
marion 66,396 Punch Card
medina 161,641 Punch Card
meigs 23,242 Punch Card
mercer 40,933 Punch Card
miami 100,230 Op-Scan
monroe 14,927 Punch Card
montgomery 552,187 Punch Card
morgan 14,843 Punch Card
morrow 33,568 Punch Card
muskingum 85,423 Punch Card
noble 14,054 Punch Card
ottawa 41,192 Op-Scan
paulding 19,665 Punch Card
perry 35,074 Punch Card
pickaway 51,723 E-Vote
pike 28,194 Punch Card
portage 154,870 Punch Card
preble 42,417 Punch Card
putnam 34,754 Punch Card
richland 128,267 Punch Card
ross 74,424 E-Vote
sandusky 61,753 Op-Scan
scioto 77,453 Punch Card
seneca 57,734 Punch Card
shelby 48,566 Punch Card
stark 377,519 Punch Card
summit 546,773 Punch Card
trumbull 221,785 Punch Card
tuscarawas 91,706 Punch Card
union 43,750 Punch Card
van wert 29,277 Punch Card
vinton 13,231 Punch Card
warren 181,743 Punch Card
washington 62,505 Op-Scan
wayne 113,121 Punch Card
williams 38,802 Punch Card
wood 123,020 Punch Card
wyandot 22,826 Punch Card
Source: Ohio 2004 Presidential Elections: Results, Summary, Charts and Spreadsheets
http://jqjacobs.net/politics/ohio_spreadsheets.htmlOhio 2004 Presidential Election Canvass - Voting by Counties - 805 Kb Excel file.
http://jqjacobs.net/politics/xls/ohio_vote_county.xls