FRANKFORT, Ky. (WHAS11) -- Six weeks after she lost her own bid for the U-S Senate, Secretary of State Alison Lundergan Grimes (D-Kentucky) tells WHAS11 if U.S. Sen. Rand Paul (R-Kentucky) tries to appear on the same ballot for both Senate and President in 2016, she will challenge him in court.

"The law is clear," Grimes said. "You can't be on the ballot twice for two offices."

Kentucky Democrats are not cooperating as Paul considers mounting simultaneous campaigns for Senate and President. Democrats maintained control of the Kentucky House in last month's election, a roadblock to legislation favored by the Republican Senate to remove the prohibition. House Speaker Greg Stumbo (D-Prestonsburg) declined to consider a Senate bill to that effect earlier this year.

Paul may challenge the law in court as the Republican Party of Kentucky also discusses whether to hold a presidential caucus rather than a primary, which would allow Paul to follow the letter of the law by not appearing on the primary ballot, twice.

"We haven't made a final decision one way or another," Paul told WHAS11 last month, "other than I have decided I am going to run for reelection for the US Senate."

Grimes was asked about the potential battle after a meeting at Kentucky's Board of Elections on Tuesday.

READ: Grimes has 'bigger plan' after losing Senate race, yet still undecided

"I will not be bullied," Grimes said. "I think hopefully the people of Kentucky understand that over the course of this past year, and I will not hesitate to seek help and assistance in the opinion of a court."

Pressed whether she would also seek an opinion from Kentucky Attorney General Jack Conway (D), who lost to Paul in the 2010 Senate race, Grimes reiterated that she would rely on the courts.

"We'll look to the court for any guidance that is needed," Grimes said. "And at the end of the day, we're not going to be bullied. I've done my job as Secretary of State for the people of Kentucky and I'll continue to do that."

But a member of Kentucky Senate leadership says there's lots of precedence for simultaneous races in other states, including U.S. Rep. Paul Ryan (R-WI) running for reelection and Vice-President in 2012 and Vice-President Joe Biden running for reelection to his Senate seat and Barack Obama's running mate in 2008.

The precedent was set when the Texas legislature changed its state law to allow Lyndon Johnson to run for both Vice-President and Senate in 1960.

"So it's a Democratic idea," said Senate Majority Floor Leader Damon Thayer (R-Georgetown). "I don't understand what the problem is."

Thayer said it is "likely" the Republican senate will again try to change the law in 2015.

"And the fact that the Senate has already passed a bill, just having one chamber take action on it probably helps Paul's legal case, should there be one," Thayer said.

It looks increasingly like there will be one.