Speaking to reporters here, DMK Working President Mr Stalin said the party has filed a case in the High Court.
He said the court has been approached so that Governor C Vidyasagar Rao take a decision based on democratic principles.
On Sunday, Mr Stalin led a delegation of opposition parties and urged Mr Rao to convene the state assembly within a week so that the Palaniswami government can prove its majority.
"We urged the governor to convene the assembly within a week. If it is not done then we will approach the court and also the people's court," he had said.
According to Mr Stalin, the DMK, with 89 legislators, along with its allies - Congress(8), IUML (1) - had a total of 98 legislators.
Stalin had said 21 legislators belonging to AIADMK Deputy General Secretary TTV Dinakaran are opposed to Chief Minister Palaniswami.
In the 235-member Assembly there are now 234 members including one nominated member without voting right.
One seat remains vacant following the death of former Chief Minister J Jayalalithaa last year.
Effectively the number of legislators with voting rights in the assembly is 233.
The number of legislators who are opposed to the government is 119 -- DMK and allies 98, Dinakaran faction 21.
"The ruling party has the support of only 114 legislators," Mr Stalin said.
"Only a democratically elected government, which has the support of majority of elected representatives, is mandated by the Constitution of India and this is recognised as a basic feature of our Parliamentary democracy," Mr Stalin told Mr Rao in his letter on Sunday.
In his letter to Mr Rao, the DMK leader said it is mandatory on the part of the governor to hold the floor test immediately and without any further delay.
"If the present minority government is allowed by your good self to continue any further, it goes against the very basic constitutional tenets of parliamentary democracy and against the constitutional principles laid down by the Supreme Court," Mr Stalin told Mr Rao.
In his letter, Mr Stalin said any delay in directing an immediate floor test will only encourage horse trading and foster unsavoury political manipulations in Tamil Nadu.
On Saturday, Tamil Nadu Chief Minister K Palaniswami claimed that with 134 legislators the AIADMK commands majority in the assembly.