A defiant Mayor Bloomberg refused Sunday to say he's sorry for failing to make public the domestic violence arrest of former Deputy Mayor Stephen Goldsmith -- and then promptly headed to the Hamptons.  "I make no apologies for either the fact that Mr. Goldsmith has left city service or for treating the Goldsmith family with basic decency as he left," Bloomberg said after days of ducking questions about the scandal.  The mayor said he figured the truth would eventutally come out about his top deputy's domestic violence arrest in Washington on July 30 - but figured there was no reason it had to come from him.  But since the news broke last Thursday, the usually available Mayor Mike had been dodging questions about Goldsmith's political face-plant, cancelling a hurricane-related news conference Thursday and then skipping out on his regular Friday radio show.  Goldsmith defended Bloomberg's handling of the matter.  "I , not the Mayor, should have more fully disclosed the reasons for my resignation," he said. "The lack of a fuller disclosure I now regret as I regret the loss of my public service career and the intrusion my children have experienced.  "I regret the criticism of the Mayor for his support of my family."  READ THE FULL TEXT OF GOLDSMITH'S STATEMENT  If Goldsmith hadn't resigned the day after the arrest, the then-deputy mayor for operations would have been fired after a mere 14 months in office, Bloomberg said.  "Upon learning of Mr. Goldsmith's arrest I made two decisions, the first was that given the high standards we set for government and the serious circumstances surrounding his arrest, Mr. Goldsmith could no longer continue to work at City Hall," Bloomberg said.  "The second was that I did not believe it was right for our administration to put out a story about an incident that had potential to be even more suffering to the Goldsmith family."  Bloomberg backhanded accusations of a cover-up.  "I have long believed that public officials who are all too willing to humiliate the people who work for them whenever its politically convenient or advantageous is an outrage and I refuse to play that game," Bloomberg said.  The city routinely makes public arrests of employees of all ranks - including the Aug. 16th arrest of a school safety agent on aggravated harassment charges.  "It's not my responsibility to spread a story," the mayor said, before heading off to Bridgehampton, LI for the Hampton Classic Horse Show with gal pal Diana Taylor.  Manhattan Borough President Scott Stringer disagreed - and called for an investigation.  "Unfortunately the Mayor has this backwards: His first obligation is to protect the public, not to protect a staff member," he said.  "The City Council should hold hearings," he said, "so we can get a full accounting of the facts in this matter."  Hizzoner, however, said he choose ignorance about Goldsmith's case - on purpose.  "We have never talked to anybody in Washington," he said. "We are very careful to never discuss what was going on in Washington because it would be totally inappropriate and there could be an allegation that we tried to influence the decisions being made down there and for that reason I did not inform our Department of Investigation or our Police Department."  Goldsmith would still be deputy mayor if it wasn't for the arrest, Bloomberg said, regardless of the city's much-criticized response to a crippling blizzard in December.  The 64-year-old former Mayor of Indianapolis left his NYC post after his current wife Margaret, 59, called 911 from their Washington townhouse after a nasty argument late Saturday July 30.  His wife told cops Goldsmith smashed her phone and grabbed her when she threatened to call police, refusing to let go until she dug her nails into his arm.  She declined to press charges when the cops arrived, but Goldsmith was taken into custody because Washington law mandates an arrest in domestic abuse calls. Later she got prosecutors to drop the case.  The mayor spoke about jobs, education and curbing gun violence to several hundred Christian Cultural Center members during their two-hour service.  Afterward, church members spouted mixed opinions about the Goldsmith fallout.  "It was like he was protecting him," said Thomasina Counts, 81, of Jamaica, Queens. "We may never get all the facts. Put it all out. Put it all out in the open."  But other congregants approved of the mayors actions.  "It's a private matter. For him to make a statement, it could have been taken out of context," said John Cortijio, 55, an IT professional from Riverdale. "The mayor can't get involved in every single employee's affairs. He's got bigger things to deal with."  With Alison Gendar and Debbie Tuma
A defiant Mayor Bloomberg said Sunday he's not sorry for keeping mum on the arrest that led to Deputy Mayor Stephen Goldsmith's sudden departure.