He died on Wednesday night in Roscommon.
Offaly County Council has set up an online Book of Condolence to allow the people to express their sympathies to the family of Detective Garda Colm Horkan.
Cathaoirleach of Offaly County Council Cllr. John Carroll opened the online initiative on http://www.offaly.ie/bookofcondolence.
All messages of sympathy will be printed and forwarded in a Book of Condolence to his family.
It will close on Friday 26th of June.
Meanwhile, a man will appear in court again next week charged in connection to the murder of Detective Garda Colm Horkan.
The officer died on Wednesday night in Castlerea, Roscommon.
Stephen Silver of Aughaward, Foxford in county Mayo was brought before a special sitting of Castlerea District Court last night.
The 43-year-old made no reply when he was charged with the murder of 49-year-old Detective Garda Horkan.
The officers death followed a violent incident in Castlerea town on Wednesday.
Mr Silver kept his head down for much of the proceedings - but did say "unreal." and I had no firearm.
His solicitor asked for all appropriate medical assessments be carried out - and free legal aid was granted.
He will appear again on Friday at Harristown District Court via video link, and has been remanded in custody.
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