(a) It shall be the duty of the county board of tax assessors to investigate diligently and to inquire into the property owned in the county for the purpose of ascertaining what real and personal property is subject to taxation in the county and to require the proper return of the property for taxation. The board shall make such investigation as may be necessary to determine the value of any property upon which for any reason all taxes due the state or the county have not been paid in full as required by law. In all cases where the full amount of taxes due the state or county has not been paid, the board shall assess against the owner, if known, and against the property, if the owner is not known, the full amount of taxes which has accrued and which may not have been paid at any time within the statute of limitations. In all cases where taxes are assessed against the owner of property, the board may proceed to assess the taxes against the owner of the property according to the best information obtainable; and such assessment, if otherwise lawful, shall constitute a valid lien against the property so assessed.

(b)(1) In all cases where unreturned property is assessed by the county board of tax assessors after the time provided by law for making tax returns has expired, the board shall add to the amount of state and county taxes due a penalty of 10 percent of the amount of the tax due or, if the principal sum of the tax so assessed is less than $10.00 in amount, a penalty of $1.00. The penalty provided in this subsection shall be collected by the tax collector or the tax commissioner and in all cases shall be paid into the county treasury and shall remain the property of the county.

(2)(A) The provisions of paragraph (1) of this subsection to the contrary notwithstanding, this paragraph shall apply with respect to counties having a population of 600,000 or more according to the United States decennial census of 1970 or any future such census.

(B) In all cases in which unreturned property is assessed by the board after the time provided by law for making tax returns has expired, the board shall add to the assessment of the property a penalty of 10 percent, which shall be included as a part of the taxable value for the year.

(c) Real property, the value of which was established by an appeal in any year, that has not been returned by the taxpayer at a different value during the next two successive years, may not be changed by the board of tax assessors during such two years for the sole purpose of changing the valuation established or decision rendered in an appeal to the board of equalization or superior court. In such cases, before changing such value or decision, the board of assessors shall first conduct an investigation into factors currently affecting the fair market value. The investigation necessary shall include, but not be limited to, a visual on-site inspection of the property to ascertain if there have been any additions, deletions, or improvements to such property or the occurrence of other factors that might affect the current fair market value and a review to determine if there are any errors in the description and characterization of such property in the files and records of the board of tax assessors. (d) When real or personal property is located within a municipality whose boundaries extend into more than one county, it shall be the duty of each board of tax assessors of a county, wherein a portion of the municipality lies, to cooperatively investigate diligently into whether the valuation of such property is uniformly assessed with other properties located within the municipality but outside the county where such property is located. Such investigation shall include, but is not limited to, an analysis of the assessment to sales ratio of properties that have recently sold within the municipality and a comparison of the average assessment level of such properties by the various counties wherein a portion of the municipality lies. The respective boards shall exchange such information as will facilitate this investigation and make any necessary adjustments to the assessment of the real and personal property that is located in their respective counties within the municipality to achieve a uniform assessment of such property throughout the municipality. Any uniformity adjustments pursuant to this subsection shall only apply to the assessment used for municipal ad valorem tax purposes within the applicable county.