It's a tale of the party versus the paper over the pooch. On Tuesday, Germany's Bild newspaper — never averse to attention-grabbing, if sometimes misleading headlines — led with a story that a three-year-old dog named Lima had joined the Social Democratic Party (SPD) and received a ballot asking her to vote on the SPD's coalition agreement with Angela Merkel's conservatives.

The party is asking its 460,000-plus members to ratify the deal before entering into another junior partnership with Merkel. Roughly 25,000 new members signed on before the deadline on February 6 to be eligible to vote on the agreement. Critics object that the procedure gives a small group of people undue influence over the next German government and is open to abuse.

Bild filled out the membership application form for Lima as a way of underscoring those points, much to the amusement of many Germans. But the SPD wasn't laughing.

Read more: Opinion: Is this the end of Germany's SPD?

The party, wracked by internal divisions over the prospect of another coalition with Merkel and sinking to historic lows in public opinion polls, immediately denied that Lima would have been able to vote. In a statement, the SPD executive board said that to be valid, all ballots in the vote, which runs until March 2, must be accompanied by a signed affidavit as to the voter's identity.

"The basic message of the story 'This dog is allowed to vote on the grand coalition' is wrong," the party executive wrote.

Pets, the party argues, can't sign and thus can't vote unless someone forges the document — a serious crime in Germany. And the conflict doesn't stop there.

The vote between human coalition detractors and supporters is expected to be close

An illicit form of journalistic research?

The SPD sees its procedure of asking ordinary members — party leaders and delegates approve coalition deals for conservatives — as particularly democratic. Bild, the party protests, is trying to make that sort of direct democratic exercise look ridiculous.

And the Social Democrats also announced that they would file an official complaint with the German Press Council, claiming that the newspaper has violated good practice by failing to identify the stunt with Lima as a piece of journalistic research.

"Especially in times of fake news and accusations that the media lies, the rules have to be abided by," SPD media attorney Christian Schertz wrote in the statement. "They were violated here."

But while the SPD's irritation may run deep, it's not particularly swift. As of Wednesday afternoon, the Press Council said that it had not received any complaint from the SPD, although one had been filed by another entity.

In any case, the Bild newspaper, which in the past has pushed far harder legal boundaries in pursuit of marketable stories, is unlikely to be deterred by the threat of an official public sanction — without any further punishment.

Lima won't get to put her paw mark on this ballot

Ballots for dogs and subscriptions for hamsters

In any case, the Wednesday edition of the paper further stoked the conflict with an article citing two legal experts, who called the SPD's plebiscite among its members "not very watertight legally" and "open to manipulation."

Theoretically it would be possible for people who wanted to create further political uncertainty in Germany to join the SPD and cast votes that would further that end.

SPD leaders admit that the party will not scrutinize every one of the hundreds of thousands of votes it expects to receive in the coming days. But they say it will investigate any suspected doubts in individual cases. That led Bild to characterize the SPD leadership as "more hoping than knowing."

Perhaps the most creative response to this dogged affair came from Melanie Amann, a journalist for the highbrow magazine Spiegel that is often seen as the polar opposite of the populist Bild. She wrote on Twitter that her pet hamster had taken out a year's subscription to the newspaper.